2. How long does it take for these two train to completely pass each other? 80.0 m long

Size: px
Start display at page:

Download "2. How long does it take for these two train to completely pass each other? 80.0 m long"

Transcription

1 Exercises 1. A rain 300. meres long is raelling a 25.0 m/s when i passes a 100. m long rain raelling a 10.0 m/s in he same direcion. How long does i ake for he longer rain o compleely pass he shorer? (26.7 seconds) 2. How long does i ake for hese wo rain o compleely pass each oher? 120. m long 10.0 m/s 6.00 m/s 80.0 m long 260. m (28.8 sec) 3. Rocke cars drie oer a 1.0 kilomeer long course and ry o break he sound barrier (330 m/s). How long would i ake such a car o rael he lengh of he rack? (3.0 seconds) 4. The Earh raels around he sun in a circle of radius 150. million km and does a complee cycle in abou 365 days. Find is speed. ( m/s) 5. Fill in he char and graph for = (+5 î ) m/s wih a saring posiion of (-8 î ) meres ( 8m Wes) ime 0 seconds 1 second 2 second 3 second posiion (-8 î ) meres = x(mere) posiion x(mere) posiion 6. Wha does i mean o say ha an objec has a) negaie posiion? b) negaie elociy? 7. Gie an example (draw a diagram) of an objec wih posiie posiion and negaie consan elociy Physics 12 Suden Workbook 9

2 8. Is he magniude of speed always he same as he magniude of elociy? YES or NO Explain your answer using relean principles of physics. 9. Mix and Mach speeds human walking fases human running op figher je ligh car on ciy sree formula-1 race car sound fases animal erminal elociy-human 330 m/s 220 kph 4 kph 10 m/s 50 kph 3600 kph km/s 55 m/s 100 kph 10. Consider he following elociy-ime graph. Find he indicaed area ogeher wih unis and explain wha his area ells you. (12.5 m disance) (m/s) elociy 2.5 m/s 1s area 2s 3 s 4s 5s 11. How long does i ake ligh (300. million meres per second) o rael from he Sun o he Earh (150. million km)? Answer in minues (8.33 minues) 12. If you glance away for 0.75 seconds while you are raelling on he highway a 120 kph, how far does he car rael in ha ime? ( 25 m) Physics 12 Suden Workbook 10

3 Exercises 1. A car raels a 20.0 m/s for 12.0 seconds, hen 10.0 m/s for 20.0 seconds hen 30.0 m/s for 6.00 seconds (all in he same direcion) a) skech a graph of he car's speed s ime b) skech a graph of he car's posiion s ime c) find he oal disance raelled (620. m) d) find he aerage speed of he car (16.3 m/s) 2. A car leaes Vancouer for Hope, a oal disance of 175 km. The drier needs o complee he rip in 3.00 hours, bu spends he firs 100. kilomeers in raffic moing a 40.0 kph. How fas does he drier need o moe o complee he rip on ime? (150. kph) 3. A car raels Eas for 20.0 seconds a 4.00 m/s, hen Wes a 5.00 m/s for 75.0 meres, hen Eas again for 15.0 seconds, coering 60.0 meres. a) find he oal disance (215 m) b) find he oal displacemen (65.0m Eas OR (+65.0 î ) meres c) find he aerage speed (4.30 m/s) d) find he aerage elociy (+1.30 î ) m/s 4. Consider he insrumens on your car dashboard a) does he speedomeer really measure speed, or does i measure elociy? b) explain your answer o a) c) does he odomeer measure disance or displacemen? d) explain your answer o c) 5. Describe he moion depiced by his graph and fill in he missing graph x 6. An objec moes 100. km o he Eas a 30.0 kph, hen moes Wes for minues. If he aerage speed for he rip is 35.0 kph, hen where does he objec end up? (assume i sared a posiion 0.0 meres) ( 13.3 km Eas or +î ) 7. A car raels 120. km Eas a 45.0 km/hr, hen goes Wes 50.0 km a 70.0 km/hr, hen goes Eas again for ime a 40.0 km/hr. If he aerage elociy for he enire rip is 30.0 km/hr Eas, find he ime (3.14 hrs) 8. Skech a - and x- graph for #7. 9. A ruck goes up a long hill a 40 kph and down he oher side (equal lengh) a 60 kph. Which of he following could be he aerage speed? a) 50 kph b) 48 kph c) 52 kph Explain your answer using relean physics principles Physics 12 Suden Workbook 14

4 Exercises 1. A dropped objec will sar a res and accelerae due o graiy: a = (-9.80 j^) m/s 2 a) Fill in he elociy char below for a dropped objec b) graph elociy-ime ime elociy 0 second 1 second 2 second 3 second 4 second 2. Describe he moion and produce he missing graph. x c) x 3. Wha happens o he moion of an objec if a) he objec is moing Eas and he acceleraion is Wes b) he objec is falling and acceleraing upwards c) he objec is moing up and acceleraing up Physics 12 Suden Workbook 19

5 4. Describe he moion represened by his graph For he preious graph, deermine a) greaes disance from origin b) displacemen beween 1s and 3s c) disance raelled beween 0s and 4s d) elociy a 3 s e) aerage elociy beween 0 and 4 s. f) maximum elociy g) acceleraion a 3 s h) ag acceleraion beween 3s and 5s (6m: 3.5 m; 6 m; 1 m/s; 1.5 m/s; 2 m/s; -1m/s^2; -1m/s^2) 6. A wha imes is his objec a) moing Eas b) moing Wes c) sopped 5 7. Which of he following bes represens he posiion-ime graph for #6 a) b) c) d) x x x x 8. Produce graphs of posiion-ime and elociy ime for an objec ha sars a res, speeds up o a maximum speed and hen immediaely begins slowing down o res. 9. A car moing a 20.0 m/s Eas deceleraes (acceleraes opposie o he direcion of moion) unil he car sops. If he deceleraion is 4 m/s 2, produce a elociy ime graph showing how long i akes he car o sop. Physics 12 Suden Workbook 20

6 Exercises 1. A dolphin acceleraes from 1.0 m/s o 7.6 m/s in 5.5 seconds. Find a) he acceleraion b) he disance raelled (1.2 m/s 2 ; 24 m) 2. A car moing a 30.0 m/s o he righ slows down (acceleraes o he lef) a 9.80 m/s 2. How far does he car go before sopping? (45.9 m) 3. A car raels a 15 m/s and speeds up uniformly. Oer he nex 5 seconds, i raels 85 m. Find he acceleraion (0.8 m/s 2 ) 4. A bungee jumper moing down a 5 m/s ends up moing upwards a 8 m/s 2.0 seconds laer. a) find he acceleraion (+6.5 m/s 2 j^) b) why is he acceleraion no 1.5 m/s 2? 5. A car sars a res and acceleraes in 4 seconds o a speed of 20 m/s, which i mainains for he nex 8 seconds. Find he oal disance raelled. (200m) 6. A rain sars a res and acceleraes a m/s 2. Afer 5.00 seconds, find is speed and disance raelled. (1.25 m/s; 3.12 m) 7. a) Subsiue he elociy formula f = i + a ino he displacemen formula d = f+ i 2 and proe ha d = i a 2 b) inerpre his displacemen formula 8. A child slides down a playground slide, acceleraing from res and raelling 6.00 meres in 4.50 seconds. When hey hi he ground, heir legs bend 20.0 cm as he child sops. Wha is he child's acceleraion in sopping? (17.7 m/s 2 ) 9. How long does i ake a 150m long rain moing a 120 kph o pass a 100. m long rain moing a 100. kph in he a) same direcion b) opposie direcion (45 s; 4.1 s) 10. Two cars are a res, facing each oher, and 200. meres apar. 1 2 If car 1 acceleraes a 6.00 m/s 2 up o maximum speed of 30.0 m/s and car 2 acceleraes a 5.00 m/s 2 up o a maximum speed of 35.0 m/s, how long does i ake he cars o mee? (6.08 s) 11. Proe ha: 2 f - 2 i = 2 a d Physics 12 Suden Workbook 26

7 Exercises 1. A mass is dropped from a 55.0 m high cliff. Find a) ime o fall b) speed a impac c) elociy a impac (3.35 sec; 32.8 m/s j^ m/s) 2. A mass is dropped from a 30.0 m high cliff, When i his he ground, i sops in seconds. Find a) ime o fall b) speed a impac c) acceleraion (and dir'n) during impac (2.47 s; 24.2 m/s; +485 j^m/s 2 ) 3. On leel ground, a mass is hrown sraigh up a 25 m/s. If we ignore air resisance, hen find a) oal ime in air b) ime o op c) maximum heigh (5.1 s; 2.6 s; 32 m) 4. A projecile is hrown sraigh up a elociy. If he acceleraion is (-g j^) m/s 2 hen find an expression for a) oal ime in air b) ime o op c) maximum heigh (2/g; /g; 2 /2g) 5. A mass is hrown sraigh up a 25 m/s. A wha imes will he speed be 18 m/s? (0.71 sec rising; 4.4 s falling) 6. A suden bends her knees 15.0 cm and jumps up 80.0 cm off he ground. Find a) he elociy wih which he suden leaes he ground b) he acceleraion of he suden while on he ground (3.96 m/s; 52.3 m/s 2 ) 7. From he edge of a 18.0 m high cliff, a rock is hrown sraigh up a 25.0 m/s so ha i falls o he base of he cliff. Find he oal ime of fligh (5.74 s) 8. From he edge of a 25 m high cliff, a rock is hrown sraigh up a 12 m/s so ha i falls o he base of he cliff. Find a) oal fligh ime b) speed a impac c) max heigh (3.8 s; 25 m/s; 32 m aboe base of cliff) 9. From he edge of a 40.0 m high cliff, a rock is hrown sraigh up a 8.00 m/s so ha i falls o he base of he cliff. Find he ime and posiion of he rock when is speed is 14.0 m/s. (2.24 s; 6.73 m below cliff OR 33.3 m aboe base) 10. From he edge of a 30.0 m high cliff a mass is hrown downwards a 5.00 m/s. Find he ime i akes o hi he ground. (2.02 sec) 11. From he op of a 30.m high cliff a rock is dropped. A he same insan from he base of he cliff, anoher rock is hrown upwards a 40. m/s. A which ime and locaion do he rocks pass each oher? (0.75 sec; 2.8 m below cliff edge) 12. A mass is hrown upwards a 29.4 m/s. Plo a graph of elociy ersus ime (saring and ending wih he objec a res). 13. A runner sars a res and acceleraes up o op speed () in 50. meres, hen runs anoher 50. m a his maximum speed (). If he ime for he race is 15s, find he maximum speed (10. m/s) 14. A rock is hrown sraigh up ino he sky. A wha poin is i acceleraion zero? a) as i rises b) a he op c) as i falls d) neer Physics 12 Suden Workbook 31

8 Exercises 1. Gien = 3.0 m/s 20. S of E draw and gie he measure of a) 2 b) - (6.0m/s a 20 SofE; 3 m/s a 20 NofW) 2. If x = 2.00 N SW and y = 3.00 N 10.0 N of W hen find: a) x + y b) 2x + y c) y - x d) 2x - y ( SofW; SofW; 51.5 NofW; 3.35 N@ 87.8 SofE) 3. Gien: A = 3.00 cm a 60.0 N of E B = 7.00 cm a 40.0 W of N C = 6.00 cm a 60.0 S of E D = 4.00 cm W Draw and measure he sum: A + B + C + D ( 4.86 cm a 34.6 N of W) 4. Add he ecors: d1= 6.0 cm a 30. N of E d2 = 5.0 cm a 40. E of S (8.4 cm a 5.6 S of E) 5. Sole for A gien ha A + B = C ; B = 10. N 20. S of E; C = 8.0 N a 25 S of E (2.1 N@ 1.0 N ofw) 6. An objec is moing a i = 3.0 m/s Eas. I acceleraes for 2.0 seconds a a = 2.0 m/s 2 Norh. a) find f by adding i and a (5.0 m/s a 53 N of E) b) why is f no 7.0 m/s? 7. Gien i = 40. m/s E f = 30. m/s S = 5.0 s a) find a = ( f - i ) / b) why is a no -2 m/s 2? (10. m/s 2 a 38 S of W) 8. Add boa/plane elociy o wind/waer elociy o find resulan elociy. Vboa + W = Vresul a) A boa has an engine speed of 7.00 m/s Norh. The waer curren is flowing a 5.00 m/s Wes. Find he resuling elociy. ( 8.60 m/s a 35.5 W of N) b) A boa ha moes a 5.00 m/s in sill waer is heading Souh. I encouners a curren of 2.00 m/s Wes. Find he resuling elociy. (5.39 m/s 21.8 W ofs) c) A plane has an airspeed of 300. kph NE. The wind is blowing a 50.0 kph S. Find he resuling elociy. ( 267 kph a 37.4 NofE) d) A plane is heading a 450. kph 25.0 E of N. The wind is blowing a 70.0 kph E. Find he resuling elociy. (483 kph a 57.5 N of E) 9. A mass is hrown sraigh up a 10. m/s. A wha imes will i be a heigh 5.0 m off he ground? (0.88 s; 1.2 s) Physics 12 Suden Workbook 37

9 Exercises 1. Coner o componens a) 50.0 m/s a 30.0 N of E (43.3î+25.0j^) b) 25.0 m/s, 40.0 S of E (19.2î j^) c) 75.0 m a 40. S of W (-57.4î j^) 2. Coner o polar he following elociies of a projecile 30.0 j 25.0 i 25.0i (39.0 m/s, 50.2 aboe hznl 25.0 m/s hznl 39.0 m/s, 50.2 below hzl 51.5 m/s, 60.9 below hznl) 25.0 i -30.0j 25.0i -45.0j 3. Gien A = 20.0 m, 30.0 N of E B = 10.0 m, 20.0 W of S a) coner boh ecors o recangular componens b) add he ecors in recangular c) coner he answer o polar form d) make a rough scale drawing of A + B o confirm your answer o c) (17.3î j^; -3.42î j^; 13.9î + 0.6j^ ; 13.9 a 2.48 NofE) 4. Gien i = 10. î j^ m/s a = -10. j^ m/s 2 = 3.0 s, find in componens a) he ecor a b) he ecor f = i + a (-30.j^ ; 10. î - 10.j^) 5. Gien i = 40. m/s S f = 30. m/s W = 5.0 s a) wrie boh ecors in recangular b) find f - i in recangular c) find a in recangular d) change o polar a (-40.j^; -30.î; -30.î + 40.j^; -6.0î + 8.0j^; 10. m/s 2 53 N of W) Physics 12 Suden Workbook 42

10 6. Add boa/plane elociy V boa o wind/waer elociy W o find resulan elociy V resul. a) A plane raels souheas a 400. kph. The wind is blowing wes a 80.0 kph. Find he plane's elociy relaie o he ground. b) A plane heads 40. W of N a an airspeed of 380 kph. The plane is seen o moe a 10. W of N a 350 kph. Wha is he wind elociy? a) (283î - 283j^) + (-80î+0j^) = 203î -283 j^= 348 kph a 54.4 S of E b) (-60.8i^+345 j^) - (-244i^+291 j^) = 183i^+ 54j^= 190kph a 16 NofE 7. Fred and Wilma leae heir house a he same ime heading for he bus sop 100. m away. Fred sars a res, acceleraes a m/s 2 up o a maximum speed of 5.00 m/s, which he holds as he runs for he bus sop. Wilma gies Fred a 5.00 second head sar and hen acceleraes for 6.00 seconds up o her maximum speed of 6.00 m/s. Who ges o he bus sop firs, and how long do hey wai for he second person o arrie? (Wilma akes 24.7s; Fred akes 25.0 s) 8. A car sars a res and acceleraes in 7.00 seconds up o a maximum speed of 30.0 m/s, and holds his speed for anoher 25.0 seconds. a) find he oal disance raelled (855 m) b) find he aerage speed (26.7 m/s) 9. Make a graph of x- and - for he car in quesion #8 10. By means of a scale drawing find: a) A + B b) A - B A = 100. m, 40. N of W B = 80. m, 10. E of S (64 m a 13 S of W; 170 m a 58 N of W) 11. Consider he following ecors A = 80.0 m, 20.0 N of W B = 55.0 m, SW a) find heir componens (-75.2î j; -38.9î j) b) find A + B (115. m, 5.77 S of W) c) find A - B (75.5 m; 61.3 N of W) Physics 12 Suden Workbook 43

11 Problems 1. A boa heads direcly across a curren flowing 2.0m/s Souh. he boa is moing a 5.0 m/s owards he Eas. Find he resulan elociy (and direcion) relaie o he ground. (5.4 m/s a 22 SofE) 2. A boa wih an engine speed of 10. kph is moing sraigh across a rier wih a 8.0 kph curren a) A wha angle is he boa poining? (53 upsream) b) Wha is he boas resulan speed? ( 6.0 kph) 3. Draw a precise ecor diagram for he following a) a plane flies a 350. m/s a 25 Nof E and he wind blows a 120. m/s Souh. b) A boa heads direcly across a 4.0 m/s curren a a speed of 7.0 m/s c) A plane flies a 250 m/s a 35 Nof E and he wind is 90.m/s a 70 E of S d) a plane has a resulan elociy of 550 m/s NE and airspeed 350 m/s Eas e) A person wans o cross a 60m wide rier (curren 3.0m/s) in 12 seconds. (assume he swimmer crosses as quickly as possible) f) a boa wans o go a 40. m/s and 25 SofE in a curren of 25 m/s a 35 NofE 4. In 3a) find he resulan elociy (& dir'n) for he plane: a plane flies a 350. m/s a 25 Nof E and he wind blows a 120. m/s Souh (320 m/s a 5.0 N of E) 5. In 3b) find he resuling speed (& dir'n) for he boa: A boa heads direcly across a 4.0 m/s curren a a speed of 7.0 m/s (8.1 m/s a 30. downsream) 6. In 3c) find he resuling elociy (& dir'n) for he plane: A plane flies a 250 m/s a 35 Nof E and he wind is 90.m/s a 70. E of S (310 m/s a 21 N of E) 7. In 3d) find he elociy of he wind (& dir'n): a plane has a resulan elociy of 550 m/s NE and airspeed 350 m/s Eas (390 m/s a 84 N of E) 8. In 3e) find he swimmer speed (& dir'n): A person wans o cross a 60. m wide rier (curren 3.0m/s) in 12 seconds. (5.8 m/s a 31 downsream) 9. In 3f) find he boa speed and dir'n: a boa wans o go a 40. m/s and 25 SofE in a curren of 25 m/s a 35 NofE (35 m/s a 63 S of E) 10. The curren in a 25.0 m wide rier is 2.00 m/s owards he Eas. If you swim Souh a 5.00 m/s across he rier a) wha is your elociy wih respec o shore? b) how long does i ake you o cross he rier? c) how far downsream do you reach he oher shore? (Vr = 5.38 m/s 21.8 E of S; = 5.00s; 10.0m) Physics 12 Suden Workbook 48

12 11. The curren in a 30.0 m wide rier is 3.00 m/s owards he Norh. If you need o moe sraigh across he rier and you can swim a 4.00 m/s a) in wha direcion should you head b) how long does i ake you o cross he rier? c) how far downsream do you reach he oher shore? ( θ = 48.6 upsream; 11.3 sec; 0meres) 12. If you swim a 4.00 m/s and 70.0 upsream and in his way you moe sraigh across a rier: a) wha is he speed of he curren? b) wha is your speed relaie o he ground? ( W = 3.76 m/s Vr = 1.37 m/s) 13. A plane flies norh a 200. kph. A wind is blowing owards he norheas a 100. kph a) wha is he plane's elociy wih respec o he ground? b) in one hour, how far off course will he plane be? c) o say on course, wha direcion should he pilo head relaie o he air? (280. kph 75.4 N of E; 70.7 km off course; 20.7 W of N) 14. A plane flies 200. kph SW relaie o he air. A radar on he ground sees he plane moing a 180. kph 30.0 S of W. a) wha is he wind elociy in recangular? b) wha is he wind speed? c) wha is he wind direcion? (W = î j^= 53.4 kph a 74.3 N of W) 15. A plane has an airspeed of 300. kph and is heading 15.0 E of N. A wind blows owards he eas such ha he plane moes 25.0 E of N relaie o he ground. a) wha is he windspeed? b) wha is he groundspeed? ( W = 57.5 kph; Vr = 320. kph) 16. The curren in a 25.0 m wide rier is 2.00 m/s owards he Souh. If you can swim a 4.00 m/s in sill waer a) how long does i ake you o cross if you swim norheas relaie o he waer? b) wha is he fases ime for crossing he rier? (8.84 sec ; 6.25 s(direcly across)) 17. A plane has an airspeed of 300 kph and is heading ecor lies in quadran III. A 100 kph wind is blowing such ha he plane moes a 300 kph S wih respec o he ground. a) wha is he plane's heading? (19.2 W of S) b) wha is he wind direcion? (9.59 S of E) Physics 12 Suden Workbook 49

13 Projecile Exercises 1. Find he fligh ime and range for each of he following projeciles h a) h = 39.2 m and = 100. m/s (2.82 s, 282 m) b) h=39.2 m and = 200. m/s (2.82 s, 566 m) c) h=88.2 m and = 100. m/s (4.24 s, 424 m) d) h = 88.2 m and = 200. m/s (4.24 s, 849 m) 2. Find he fligh ime and range for hese projeciles θ a) = 100. m/s and θ= 45.0 (14.4 s, 1020m) b) = 100. m/s and θ = 60.0 (17.7 s, 884 m) c) = 200. m/s and θ= 45.0 (28.8 s, 4080 m) 3. Find he fligh ime and range of he following projeciles θ h a) h = 14.7 m = 19.6 m/s and θ = 30.0 (3.00s, 50.9m) b) h = 78.4 m = 41.6 m/s and θ = 45.0 (8.00s, 235m) 4. If a fooball player kicks a fooball so ha i spends 3.0 seconds in he air and raels 50. m, hen find he elociy and angle of he kick. (noe: picure is like #2 aboe) (22 m/s, 41 ) Physics 12 Suden Workbook 57

14 5. For he projecile picured in #3 a) find a) he horizonal elociy afer 1.30 seconds b) he erical elociy afer 1.30 seconds c) he resulan elociy afer 1.30 seconds (17.0m/s, -2.94m/s, 17.2 m/s a 9.83 below hznl) 6. For he projecile in #2a) find a) he horizonal posiion/displacemen afer 3.00 seconds b) he erical posiion afer 3.00 seconds c) he resulan displacemen afer 3.00 sec (212 m, 168 m, 271m a 38.4 from launch poin) 7. For he projecile in #1a) find he resulan elociy (& angle) jus before he projecile his he ground (104 m/s a 15.5 below hznl) 8. A projecile is launched on leel ground. Two seconds laer i is moing a 30.0 m/s a 20.0 S of E. Find is launch elociy and direcion (29.7 m/s a 18.3 aboe hznl) 9. The horizonal and erical speed of a projecile are measured in an experimen. The daa is below: ime (sec) 0.0 s 0.1 s 0.2 s 0.3 s 0.4 s 0.5 s 0.6 s x-speed(m/s) y-speed(m/s) a) graph he horizonal elociy ersus ime and draw conclusions b) graph he erical elociy ersus ime and draw conclusions 10. A projecile is launched a 30. m/s and 35 on leel ground. When i has raelled horizonally 14 meres, wha is is speed and direcion? (27 m/s a 25 aboe hznl) 11. A projecile is launched on leel ground a 25.0 m/s and a Wha is is maximum heigh? (10.5 m) 12. A projecile is launched a 35.0 m/s and a 30.0 on an 20.0 angled slope. Where does i land (disance along slope measured from launch) (42.6 m) Physics 12 Suden Workbook 58

15 Exercises and Reiew 1. A projecile is launched from a 80.0 m high cliff a a elociy of 30.0 m/s and an angle of 40.0 aboe he horizonal. Find is a) posiion (x and y) afer 3.50 sec (80.4 m righ, 7.47m up) b) elociy (resulan) afer 3.50 sec (27.4 m/s a 33.2 below hznl) 2. A projecile is launched a an angle on leel ground. Which of hese graphs is a graph of is a) horizonal displacemen s ime b) erical displacemen s ime c) erical elociy ersus ime d) horizonal elociy ersus ime i ii iii i 3. Find he speed and direcion of he projecile when i his he wall. 25 m/s m (24 m/s; 20. below hznl) 4. Wrie he equaions you would use o find he launch speed of he projecile shown below if i were o land a he poin marked x m x 30.0 m 40.0 m y (160 = cos(40) ; 30 = sin(40) ) 5. For he diagram aboe, find he launch speed of he projecile if i lands exacly half-way beween x and y. (47.3 m/s) 6. A projecile is launched horizonally off of a cliff. When i his he ground a he base of he cliff, i is moing a 50.0 m/s and 20.0 below hznl. Find he cliff heigh and range of he projecile. (14.9m; 82.0m) 7. A person walks 30.0 m a 20.0 Norh of Eas a 2.00 m/s, hen 5.00 m Eas a 1.00 m/s, hen 2.00m Norh a m/s a) how much ime elapsed? (24 s) b) wha is he resulan displacemen? (35.4 m a 20.3 N of E) c) wha is he aerage elociy? (1.47 m/s a 20.3 N of E) Physics 12 Suden Workbook 64

16 8. A boa heads direcly across a 4.0 m/s curren moing a an engine speed of 6.0 m/s. When i reaches he oher side of he 30.m wide rier a) how much ime has elapsed? (5.0 seconds) b) how far downsream is he boa? (20. m) c) wha resulan disance has i raelled? (36 m) 9. A projecile is launched on leel ground a 20. m/s and 30. aboe he hznl. Find he elociy afer 0.50 seconds by graphical ecor addiion: f = i + a (18 m/s a 16 aboe hznl) 10. The engineer of a passenger rain moing a 29.0 m/s sees a freigh rain 360.m ahead on he rack moing a 6.00 m/s. The engineer akes seconds o reac, and hen applies he brakes. A wha rae mus he passenger rain hen decelerae in order o aoid a collision? (0.754 m/s 2 ) for answers on page 66: 11. A bulle fired horizonally his he ground in 0.5 sec. If i is fired in he same direcion wih higher speed, how long will i be in he air? a) > 0.5 s b) 0.5 s c) < 0.5 s 12. Neglecing air resisance, a horizonally fired projecile mainains is horizonal componen of speed because a) i is no aced upon by any force b) i is no aced upon by any horizonal forces c) i has no erical componen of speed o begin wih d) he ne force acing on i is zero 13. A huner aims a rifle a 10 aboe he horizonal and fires. A he same insan, he huner drops a bulle from his hand while holding his rifle. The bulle o hi he ground firs will be a) dropped b) fired c) boh hi a same ime 14. If an objec is dropped, i acceleraes down a 1g. If insead i is hrown upwards and follows a parabolic pah, is acceleraion in fligh is a) 0 b) 0< a < 1 g c) 1g d) a> 1g 15. A projecile is fired on leel ground a 50 and his he ground down range. I will land in he same place if i is insead fired a a) 40 b) 45 c) 55 d) A rifle wih muzzle elociy 100m/s is fired horizonally from a ower. Afer one second, how far will he bulle hae raelled horizonally? a) 50 m b) 100m c) > 100m 17. Two projeciles are fired on leel ground wih he same speed. One is fired a 30 and he oher a 60. Which projecile his he ground firs? a) 30 b) 60 c) hi a same ime 18. An objec is hrown sraigh ino he air. If we include air resisance, hen which is greaer: he ime for he ascen(rising) or he ime for he descen (falling) a) descen b) ascen c) same Physics 12 Suden Workbook 65

17 19. A baseball is hrown horizonally from a heigh of 5 meres and i lands 20m down range. The piching speed is approximaely a) 5 m/s b) 10 m/s c) 20 m/s d) 25 m/s 20. An airplane flying horizonally a 400m/s a an aliude of 500m drops a package. How far does he package rael horizonally before landing? a) 0 km, i lands righ underneah he release poin b) 4 km c) 5 km d) > 5km 21. For a projecile launched horizonally off of a cliff, if he launch speed doubles, wha happens o he range? a) no change b) doubles c) haled d) increased by 2 e) quadrupled 22. For a projecile launched horizonally off of a cliff, if he cliff heigh doubles, wha happens o he range? a) no change b) doubles c) haled d) increased by 2 e) quadrupled 23. For a projecile launched a an angle on leel ground, if he launch speed doubles, wha happens o he he range? a) no change b) doubles c) haled d) increased by 2 e) quadrupled 24. Two projeciles are launched on leel ground a equal speeds, one a 30, he oher a 60. Which answer bes explains why hey rael he same horizonal disance? a) he 60 projecile spends less ime in he air b) heir erical disances are he same, so heir horizonal disances are also c) he 30 projecile and he 60 projecile hae he same fligh ime d) he 30 projecile has less fligh ime, bu more horizonal speed e) he 30 projecile has a greaer speed han he 60 projecile 25. A plane raelling a 100 m/s drops a package from a heigh of 500 m. When he package his he ground, wha is he disance from he plane o he package? a) 500 m b) 1000 m c) 1120 m d) > 1120 m b b a c a b a a c b b d e d a Physics 12 Suden Workbook 66

18 Lesson 11: Pracice Exam Secion I Muliple Choice 30 quesions, 1 marks each for 30 marks oal. 1. Which of he following is rue for his projecile? a) he disance raelled is zero b) he erical displacemen is zero c) he posiion is zero d) he iniial elociy is zero e) he horizonal displacemen is zero 2. Which of he following is he bes definiion of acceleraion? a) he rae of change of elociy b) he rae of change of posiion c) elociy/ime d) displacemen/ime e) change in elociy 3. A car moing a 20 m/s deceleraes a a rae of 4.0 m/s 2 when he brakes are applied. How far does he car rael before sopping? a) 5 m b) 0.2 m c) 25 m d) 100 m e) 50 m 4. If X is 3 m Eas and Y is 4m Souh, hen find X + Y a) 5 m Souheas b) 7 m Norheas c) 5 m 53 S of E d) 5 m 37 S of E e) 5 m 53 N of E 5. If X is 3 m Eas and Y is 4m Souh, hen find X - Y a) 5 m Souheas b) 7 m Norheas c) 5 m 53 S of E d) 5 m 37 S of E e) 5 m 53 N of E 6. If ecor A poins N ecor B poins E and ecor C poins S hen which of he following is A - B + C? a) b) c) d) e) 7. Change o polar he ecor F = (-2.5 î j^) N a) 1.5 N; 32 N of W b) 4.7 N; 32 N of W c) 22.5 N; 58 N of E d) 4.7 N; 58 N of E e) 4.7 N; 58 N of W 8. Change o recangular componens he ecor: a = 8.60 m/s 2 a 44 S of W a) -6.19i^ j^ b) 6.19i^ j^ c) -5.97i^- 6.19j^ d) i^ j^ e) i^ j^ Physics 12 Suden Workbook 67

19 9. If he iniial elociy of an objec is Easward and he final elociy of he objec is owards he Souh, hen wha is he direcion of he acceleraion? i f a) souh b) norhwes c) souhwes d) souheas e) norheas 10. You head direcly across a rier ha is flowing a 4.0 m/s. If you can swim a 2.0 m/s, hen wha is your elociy relaie o shore? curren heading N E a) 4.5 m/s a 63 E of N b) 6 m/s E c) 3.5 m/s a 63 E of S d) 3.5 m/s a 27 N of E e) 4.5 m/s a 27 E of N 11. A kayaker has o moe sraigh across a 20. m wide rier ha is flowing a 2.5 m/s. If he kayaker can paddle a 3.5 m/s, hen a wha angle should hey head, and how long does i ake hem o reach he oher shore? curren N kayak waerfall E 20 meres a) 44 N of E ime= 4,6 s b) 46 N of E ime= 8.2 s c) 55 N of E ime= 1.1 s d) 44 N of E ime= 8.2 s e) 46 N of E ime= 4.6 s 12. A boa heads direcly across a 30. m wide rier a a speed of 3.5 m/s. If he curren in he rier is 1.5m/s hen how far downsream is he boa when i reaches he oher shore? a) 25.8 m b) 8.6 m c) 17.2 m d) 70 m e) 12.9 m 13. A plane flies Norh a 300 kph. A wind is blowing from he wes such ha he groundspeed is 330 kph. Wha is he direcion of he elociy relaie o he ground? a) 25 W of N b) 65 E of N c) 43 E of N d) 43 W of N e) 25 E of N Physics 12 Suden Workbook 68

20 14. A plane flies wih an airspeed of 350. kph eas. The wind is blowing a 150. kph a 60 N of W. Find he resulan ground speed and direcion. a) 381 kph, 23 N of E b) 444 kph, 17 N of E c) 242 kph, 18 N of E d) 304 kph, 25 N of E e) 200 kph, NE 15. A ball rolls off he op of a 10.0 m high building a a speed of 3.00 m/s. How long does i ake o hi he ground? = 3 m/s 10m a) 3.33 s b) 2.00 s c) 1.43 s d) 0.71 s e) 1.00 s 16. In quesion 15, how far from he base of he building does he ball land? a) 3.0 m b) 9.9 m c) 4.3 m d) 6.0 m e) 29.4 m 17. In quesion 15, if he speed of he ball is doubled, wha happens o he range R? (is disance from he base of he wall) a) R is haled ( 0.5) b) R doubles ( 2) c) R is unchanged d) R is quadrupled ( 4) e) R increases by 2 ( 2 ) 18. In quesion 15, wha is he speed (resulan elociy magniude) of he ball jus before i his he ground? a) 14.6 m/s b) 14.3 m/s c) 14.0 m/s d) 29.4 m/s e) 16.7 m/s 19. A projecile is launched a an angle on leel ground. Which of he following is rue abou he resulan speed and he acceleraion of he projecile a he op of is rajecory? speed acceleraion a) posiie -9.8 b) c) 0 0 d) posiie 0 e) consan 0 Physics 12 Suden Workbook 69

21 20. A projecile is launched on leel ground as in quesion 19. The launch speed is 42.0 m/s and he launch angle is 25.0 : 42.0 m/s 25.0 Find he erical componen of he iniial elociy. a) 42.0 m/s b) 5.90 m/s c) 18.6 m/s d) 17.7 m/s e) 38.1 m/s 21. In quesion 20, find he speed of he projecile a he op of is rajecory. a) 42.0 m/s b) 5.90 m/s c) 18.6 m/s d) 17.7 m/s e) 38.1 m/s 22. In quesion 20, find he fligh ime of he projecile. a) 1.81 s b) 3.62 s c) 7.77 s d) 3.92 s e) 8.57 s 23. In quesion 20, find he range of he projecile, R. a) 67.3 m b) 163 m c) 138 m d) 68.9 m e) 149 m 24. Find he maximum heigh of his projecile aboe he base of he cliff m/s m a) 19.6 m b) 4.90 m c) 39.2 m d) 58.8 m e) 44.1 m 25. Find he fligh ime of he projecile in quesion 24. a) 1 s b) 2 s c) 4 s d) 3 s e) 3.5 s 26. A plane flying horizonally a speed drops a package. Afer 3 seconds, wha is he speed of he package in m/s? Ignore air resisance. a) 29.4 b) c) d) e) A projecile is launched a speed and angle θ >45 on fla ground. If he speed is kep consan and he angle is increased slighly, hen wha happens o he fligh ime and range? ime range a no change no change b increases decreases c increases increases d decreases no change e decreases decreases Physics 12 Suden Workbook 70

22 28. Which of he following bes describes projecile moion? horizonal moion erical moion a consan elociy consan acceleraion b zero acceleraion consan elociy c consan elociy zero elociy d zero elociy consan acceleraion e zero acceleraion zero acceleraion 29. A projecile is launched a 40 m/s and 30 aboe he horizonal from a cliff. A wha ime during he fligh will he speed be 30 m/s? a) 2.0 s b) 1.0 s c) 4.1 s d) 3.1 s e) neer 30. A projecile is launched a 40 m/s and 30 aboe he horizonal from a cliff. A wha ime during he fligh will he speed be 45 m/s? a) 5.0 s b) 0.5 s c) 4.1 s d) 2.9 s e) neer b a e c e d e a c a b e e d c c b b a d e b c e c d b a e a Physics 12 Suden Workbook 71

23 Secion II Problems 20 marks oal. 5 marks each 1. A plane has an airspeed of 410. kph in a direcion 40.0 S of E. I encouners a norherly (owards he norh) wind and is resulan moion is along 25.0 S of E. Find: a) he speed of he wind b) he resulan speed (117 kph; 346 kph) 2. For he following projecile, find: a) he polar elociy afer 2.0 s b) he posiion (x and y) afer 2.0s. y 70. m 20. m/s m x (17 m/s a 24 below hznl; (31î + 76j^) meres) 3. a) Skech a sop acion picure (3-4 frames) for he moion of he projecile below. Include elociy componens on your picure. b) explain by referring o forces why he elociy changes in his way. 4. Joe Carer his a baseball and i leaes he ba a an angle of 35.0 and a heigh of 1.00 m aboe he ground. The ball raels 100.m and barely passes oer a 12.0 m high fence. A wha speed did he ball leae he ba? home run! (35.2 m/s) Physics 12 Suden Workbook 72

24 oher (hard) pracice exam quesions 1. A projecile is launched off of a 30.m high cliff a 25 and 40. m/s. he base of he cliff is irregular as shown in he diagram. Where exacly (x and y) does he projecile land? (x=160m,y=9.2m ie 0.8m from op of 10 m wall) 40 m/s m y 160 m 10 m x 2. A gun can shoo charges a 250 m/s. The gun is 2500 m from he base of a 1800 m high mounain. For some angles, he sho will hi he mounain and no reach he enemy. Your ask is o find he range of angles for which he gun will be able o clear he mounain (eg. from 10 o 15 ). gun θ 1.8 km 2.5 km mounain (50 o 76 ) 3. A amusemen parks, here is ofen a cones inoling hrowing sofballs ino milk cans. For he sofballs o go in, hey mus ener a an angle of 80.0 below he horizonal. The op of he milk cans are 200. cm horizonally and cm erically from he hrower. A wha angle and speed should he hrower release he sofball for i o go in? cm 200 cm (7.66 m/s; 80.2 N of E) Physics 12 Suden Workbook 73

Chapter 2 Kinematics in One Dimension

Chapter 2 Kinematics in One Dimension Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how

More information

Answer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1

Answer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1 Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prin-ou should hae 1 quesions. Muliple-choice quesions may coninue on he ne column or page find all choices before making your selecion. The

More information

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m

More information

AP Physics Velocity and Linear Acceleration Unit 1 Problems:

AP Physics Velocity and Linear Acceleration Unit 1 Problems: Uni 1 Problems: Linear Velociy and Acceleraion This enire se of problems is due he day of he es. I will no accep hese for a lae grade. * = Problems we do ogeher; all oher problems are homework (bu we will

More information

Acceleration Lab Teacher s Guide

Acceleration Lab Teacher s Guide Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion

More information

Kinematics in 1-D From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, morin@physics.harvard.

Kinematics in 1-D From Problems and Solutions in Introductory Mechanics (Draft version, August 2014) David Morin, morin@physics.harvard. Chaper 2 Kinemaics in 1-D From Problems and Soluions in Inroducory Mechanics (Draf ersion, Augus 2014) Daid Morin, morin@physics.harard.edu As menioned in he preface, his book should no be hough of as

More information

Imagine a Source (S) of sound waves that emits waves having frequency f and therefore

Imagine a Source (S) of sound waves that emits waves having frequency f and therefore heoreical Noes: he oppler Eec wih ound Imagine a ource () o sound waes ha emis waes haing requency and hereore period as measured in he res rame o he ource (). his means ha any eecor () ha is no moing

More information

Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 2204 FINAL EXAMINATION. June 2009.

Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 2204 FINAL EXAMINATION. June 2009. Name: Teacher: DO NOT OPEN THE EXMINTION PPER UNTIL YOU RE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 2204 FINL EXMINTION June 2009 Value: 100% General Insrucions This examinaion consiss of wo pars. Boh pars

More information

Newton s Laws of Motion

Newton s Laws of Motion Newon s Laws of Moion MS4414 Theoreical Mechanics Firs Law velociy. In he absence of exernal forces, a body moves in a sraigh line wih consan F = 0 = v = cons. Khan Academy Newon I. Second Law body. The

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

AP Calculus BC 2010 Scoring Guidelines

AP Calculus BC 2010 Scoring Guidelines AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board

More information

Motion Along a Straight Line

Motion Along a Straight Line Moion Along a Sraigh Line On Sepember 6, 993, Dave Munday, a diesel mechanic by rade, wen over he Canadian edge of Niagara Falls for he second ime, freely falling 48 m o he waer (and rocks) below. On his

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

More information

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches. Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa

More information

Name: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling

Name: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling Name: Algebra II Review for Quiz #13 Exponenial and Logarihmic Funcions including Modeling TOPICS: -Solving Exponenial Equaions (The Mehod of Common Bases) -Solving Exponenial Equaions (Using Logarihms)

More information

RC (Resistor-Capacitor) Circuits. AP Physics C

RC (Resistor-Capacitor) Circuits. AP Physics C (Resisor-Capacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED

More information

A Curriculum Module for AP Calculus BC Curriculum Module

A Curriculum Module for AP Calculus BC Curriculum Module Vecors: A Curriculum Module for AP Calculus BC 00 Curriculum Module The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy.

More information

CHARGE AND DISCHARGE OF A CAPACITOR

CHARGE AND DISCHARGE OF A CAPACITOR REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

More information

AP Calculus AB 2013 Scoring Guidelines

AP Calculus AB 2013 Scoring Guidelines AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was

More information

Permutations and Combinations

Permutations and Combinations Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes - ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he k-value for he middle erm, divide

More information

AP Calculus AB 2010 Scoring Guidelines

AP Calculus AB 2010 Scoring Guidelines AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College

More information

AP Calculus AB 2007 Scoring Guidelines

AP Calculus AB 2007 Scoring Guidelines AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and

More information

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes

More information

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009 ull-wave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal

More information

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur Module 4 Single-phase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,

More information

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer) Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions

More information

Signal Rectification

Signal Rectification 9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, half-wae and fullwae. Le s firs consider he ideal

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

9. Capacitor and Resistor Circuits

9. Capacitor and Resistor Circuits ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren

More information

CHAPTER FIVE. Solutions for Section 5.1

CHAPTER FIVE. Solutions for Section 5.1 CHAPTER FIVE 5. SOLUTIONS 87 Soluions for Secion 5.. (a) The velociy is 3 miles/hour for he firs hours, 4 miles/hour for he ne / hour, and miles/hour for he las 4 hours. The enire rip lass + / + 4 = 6.5

More information

Lecture 2: Telegrapher Equations For Transmission Lines. Power Flow.

Lecture 2: Telegrapher Equations For Transmission Lines. Power Flow. Whies, EE 481 Lecure 2 Page 1 of 13 Lecure 2: Telegraher Equaions For Transmission Lines. Power Flow. Microsri is one mehod for making elecrical connecions in a microwae circui. I is consruced wih a ground

More information

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

More information

C Fast-Dealing Property Trading Game C

C Fast-Dealing Property Trading Game C AGES 8+ C Fas-Dealing Propery Trading Game C Y Collecor s Ediion Original MONOPOLY Game Rules plus Special Rules for his Ediion. CONTENTS Game board, 6 Collecible okens, 28 Tile Deed cards, 16 Wha he Deuce?

More information

Inductance and Transient Circuits

Inductance and Transient Circuits Chaper H Inducance and Transien Circuis Blinn College - Physics 2426 - Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual

More information

The Torsion of Thin, Open Sections

The Torsion of Thin, Open Sections EM 424: Torsion of hin secions 26 The Torsion of Thin, Open Secions The resuls we obained for he orsion of a hin recangle can also be used be used, wih some qualificaions, for oher hin open secions such

More information

C Fast-Dealing Property Trading Game C

C Fast-Dealing Property Trading Game C If you are already an experienced MONOPOLY dealer and wan a faser game, ry he rules on he back page! AGES 8+ C Fas-Dealing Propery Trading Game C Y Original MONOPOLY Game Rules plus Special Rules for his

More information

Mr. Kepple. Motion at Constant Acceleration 1D Kinematics HW#5. Name: Date: Period: (b) Distance traveled. (a) Acceleration.

Mr. Kepple. Motion at Constant Acceleration 1D Kinematics HW#5. Name: Date: Period: (b) Distance traveled. (a) Acceleration. Moion Consn Accelerion 1D Kinemics HW#5 Mr. Kepple Nme: De: Period: 1. A cr cceleres from 1 m/s o 1 m/s in 6.0 s. () Wh ws is ccelerion? (b) How fr did i rel in his ime? Assume consn ccelerion. () Accelerion

More information

HFCC Math Lab Intermediate Algebra - 13 SOLVING RATE-TIME-DISTANCE PROBLEMS

HFCC Math Lab Intermediate Algebra - 13 SOLVING RATE-TIME-DISTANCE PROBLEMS HFCC Mah Lab Inemeiae Algeba - 3 SOLVING RATE-TIME-DISTANCE PROBLEMS The vaiables involve in a moion poblem ae isance (), ae (), an ime (). These vaiables ae elae by he equaion, which can be solve fo any

More information

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17

More information

4. International Parity Conditions

4. International Parity Conditions 4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

Signal Processing and Linear Systems I

Signal Processing and Linear Systems I Sanford Universiy Summer 214-215 Signal Processing and Linear Sysems I Lecure 5: Time Domain Analysis of Coninuous Time Sysems June 3, 215 EE12A:Signal Processing and Linear Sysems I; Summer 14-15, Gibbons

More information

The Transport Equation

The Transport Equation The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be

More information

Diagnostic Examination

Diagnostic Examination Diagnosic Examinaion TOPIC XV: ENGINEERING ECONOMICS TIME LIMIT: 45 MINUTES 1. Approximaely how many years will i ake o double an invesmen a a 6% effecive annual rae? (A) 10 yr (B) 12 yr (C) 15 yr (D)

More information

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z o ffix uden abel ere uden ame chool ame isric ame/ ender emale ale onh ay ear ae of irh an eb ar pr ay un ul ug ep c ov ec as ame irs ame lace he uden abel ere ae uden denifier chool se nly rined in he

More information

INTRODUCTION TO EMAIL MARKETING PERSONALIZATION. How to increase your sales with personalized triggered emails

INTRODUCTION TO EMAIL MARKETING PERSONALIZATION. How to increase your sales with personalized triggered emails INTRODUCTION TO EMAIL MARKETING PERSONALIZATION How o increase your sales wih personalized riggered emails ECOMMERCE TRIGGERED EMAILS BEST PRACTICES Triggered emails are generaed in real ime based on each

More information

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS Hao Wu and Qinfen Zheng Cenre for Auomaion Research Dep. of Elecrical and Compuer Engineering Universiy of Maryland, College Park, MD-20742 {wh2003, qinfen}@cfar.umd.edu

More information

Exam 1 Review Questions PHY 2425 - Exam 1

Exam 1 Review Questions PHY 2425 - Exam 1 Exam 1 Review Questions PHY 2425 - Exam 1 Exam 1H Rev Ques.doc - 1 - Section: 1 7 Topic: General Properties of Vectors Type: Conceptual 1 Given vector A, the vector 3 A A) has a magnitude 3 times that

More information

Economics Honors Exam 2008 Solutions Question 5

Economics Honors Exam 2008 Solutions Question 5 Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I

More information

SOLID MECHANICS TUTORIAL GEAR SYSTEMS. This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 3.

SOLID MECHANICS TUTORIAL GEAR SYSTEMS. This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 3. SOLI MEHNIS TUTORIL GER SYSTEMS This work covers elemens of he syllabus for he Edexcel module 21722P HN/ Mechanical Principles OUTOME 3. On compleion of his shor uorial you should be able o do he following.

More information

Steps for D.C Analysis of MOSFET Circuits

Steps for D.C Analysis of MOSFET Circuits 10/22/2004 Seps for DC Analysis of MOSFET Circuis.doc 1/7 Seps for D.C Analysis of MOSFET Circuis To analyze MOSFET circui wih D.C. sources, we mus follow hese five seps: 1. ASSUME an operaing mode 2.

More information

Making Use of Gate Charge Information in MOSFET and IGBT Data Sheets

Making Use of Gate Charge Information in MOSFET and IGBT Data Sheets Making Use of ae Charge Informaion in MOSFET and IBT Daa Shees Ralph McArhur Senior Applicaions Engineer Advanced Power Technology 405 S.W. Columbia Sree Bend, Oregon 97702 Power MOSFETs and IBTs have

More information

Capacitors and inductors

Capacitors and inductors Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear

More information

Chapter 4: Exponential and Logarithmic Functions

Chapter 4: Exponential and Logarithmic Functions Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion

More information

Physics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension

Physics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension Physics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension Conceptual Questions 1) Suppose that an object travels from one point in space to another. Make

More information

1 HALF-LIFE EQUATIONS

1 HALF-LIFE EQUATIONS R.L. Hanna Page HALF-LIFE EQUATIONS The basic equaion ; he saring poin ; : wrien for ime: x / where fracion of original maerial and / number of half-lives, and / log / o calculae he age (# ears): age (half-life)

More information

SOLUTIONS RADIOLOGICAL FUNDAMENTALS PRACTICE PROBLEMS FOR TECHNICAL MAJORS

SOLUTIONS RADIOLOGICAL FUNDAMENTALS PRACTICE PROBLEMS FOR TECHNICAL MAJORS SOLUTIONS RADIOLOGICAL FUNDAMENTALS PRACTICE PROBLEMS FOR TECHNICAL MAJORS Noe: Two DOE Handbooks are used in conjuncion wih he pracice quesions and problems below o provide preparaory maerial for he NPS

More information

Special Relativity Being from Misunderstanding of Principle of Constant Speed of Light

Special Relativity Being from Misunderstanding of Principle of Constant Speed of Light Speial Relaii Being from Misundersanding of riniple of Consan Speed of Ligh Li ifeng Yanshan Uniersi Qinhuangdao Hebei 066004 China Absra Inrodues basi hpoheses and basi iewpoin of spae-ime in speial relaii.

More information

1. y 5y + 6y = 2e t Solution: Characteristic equation is r 2 5r +6 = 0, therefore r 1 = 2, r 2 = 3, and y 1 (t) = e 2t,

1. y 5y + 6y = 2e t Solution: Characteristic equation is r 2 5r +6 = 0, therefore r 1 = 2, r 2 = 3, and y 1 (t) = e 2t, Homework6 Soluions.7 In Problem hrough 4 use he mehod of variaion of parameers o find a paricular soluion of he given differenial equaion. Then check your answer by using he mehod of undeermined coeffiens..

More information

Module 3. R-L & R-C Transients. Version 2 EE IIT, Kharagpur

Module 3. R-L & R-C Transients. Version 2 EE IIT, Kharagpur Module 3 - & -C Transiens esson 0 Sudy of DC ransiens in - and -C circuis Objecives Definiion of inducance and coninuiy condiion for inducors. To undersand he rise or fall of curren in a simple series

More information

A Probability Density Function for Google s stocks

A Probability Density Function for Google s stocks A Probabiliy Densiy Funcion for Google s socks V.Dorobanu Physics Deparmen, Poliehnica Universiy of Timisoara, Romania Absrac. I is an approach o inroduce he Fokker Planck equaion as an ineresing naural

More information

THE PRESSURE DERIVATIVE

THE PRESSURE DERIVATIVE Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics THE PRESSURE DERIVATIVE The ressure derivaive has imoran diagnosic roeries. I is also imoran for making ye curve analysis more reliable.

More information

Automatic measurement and detection of GSM interferences

Automatic measurement and detection of GSM interferences Auomaic measuremen and deecion of GSM inerferences Poor speech qualiy and dropped calls in GSM neworks may be caused by inerferences as a resul of high raffic load. The radio nework analyzers from Rohde

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

Usefulness of the Forward Curve in Forecasting Oil Prices

Usefulness of the Forward Curve in Forecasting Oil Prices Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,

More information

Differential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.

Differential Equations. Solving for Impulse Response. Linear systems are often described using differential equations. Differenial Equaions Linear sysems are ofen described using differenial equaions. For example: d 2 y d 2 + 5dy + 6y f() d where f() is he inpu o he sysem and y() is he oupu. We know how o solve for y given

More information

Cointegration: The Engle and Granger approach

Cointegration: The Engle and Granger approach Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

More information

4 Convolution. Recommended Problems. x2[n] 1 2[n]

4 Convolution. Recommended Problems. x2[n] 1 2[n] 4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.

More information

MTH6121 Introduction to Mathematical Finance Lesson 5

MTH6121 Introduction to Mathematical Finance Lesson 5 26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random

More information

Pulse-Width Modulation Inverters

Pulse-Width Modulation Inverters SECTION 3.6 INVERTERS 189 Pulse-Widh Modulaion Inverers Pulse-widh modulaion is he process of modifying he widh of he pulses in a pulse rain in direc proporion o a small conrol signal; he greaer he conrol

More information

Fourier Series & The Fourier Transform

Fourier Series & The Fourier Transform Fourier Series & The Fourier Transform Wha is he Fourier Transform? Fourier Cosine Series for even funcions and Sine Series for odd funcions The coninuous limi: he Fourier ransform (and is inverse) The

More information

Caring for trees and your service

Caring for trees and your service Caring for rees and your service Line clearing helps preven ouages FPL is commied o delivering safe, reliable elecric service o our cusomers. Trees, especially palm rees, can inerfere wih power lines and

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

Present Value Methodology

Present Value Methodology Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer

More information

Return Calculation of U.S. Treasury Constant Maturity Indices

Return Calculation of U.S. Treasury Constant Maturity Indices Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion

More information

Making a Faster Cryptanalytic Time-Memory Trade-Off

Making a Faster Cryptanalytic Time-Memory Trade-Off Making a Faser Crypanalyic Time-Memory Trade-Off Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch

More information

THE LAW SOCIETY OF THE AUSTRALIAN CAPITAL TERRITORY

THE LAW SOCIETY OF THE AUSTRALIAN CAPITAL TERRITORY Complee he form in BLOCK LETTERS Provide deails on separae shees if required To Responden Address THE LAW SOCIETY OF THE AUSTRALIAN CAPITAL TERRITORY Personal Injury Claim ificaion pursuan o he Civil Law

More information

NOTES ON OSCILLOSCOPES

NOTES ON OSCILLOSCOPES NOTES ON OSCILLOSCOPES NOTES ON... OSCILLOSCOPES... Oscilloscope... Analog and Digial... Analog Oscilloscopes... Cahode Ray Oscilloscope Principles... 5 Elecron Gun... 5 The Deflecion Sysem... 6 Displaying

More information

The Derivative of a Constant is Zero

The Derivative of a Constant is Zero Sme Simple Algrihms fr Calculaing Derivaives The Derivaive f a Cnsan is Zer Suppse we are l ha x x where x is a cnsan an x represens he psiin f an bjec n a sraigh line pah, in her wrs, he isance ha he

More information

Stability. Coefficients may change over time. Evolution of the economy Policy changes

Stability. Coefficients may change over time. Evolution of the economy Policy changes Sabiliy Coefficiens may change over ime Evoluion of he economy Policy changes Time Varying Parameers y = α + x β + Coefficiens depend on he ime period If he coefficiens vary randomly and are unpredicable,

More information

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se

More information

Differential Equations and Linear Superposition

Differential Equations and Linear Superposition Differenial Equaions and Linear Superposiion Basic Idea: Provide soluion in closed form Like Inegraion, no general soluions in closed form Order of equaion: highes derivaive in equaion e.g. dy d dy 2 y

More information

Lecture 7 Force and Motion. Practice with Free-body Diagrams and Newton s Laws

Lecture 7 Force and Motion. Practice with Free-body Diagrams and Newton s Laws Lecture 7 Force and Motion Practice with Free-body Diagrams and Newton s Laws oday we ll just work through as many examples as we can utilizing Newton s Laws and free-body diagrams. Example 1: An eleator

More information

Chapter 6 Interest Rates and Bond Valuation

Chapter 6 Interest Rates and Bond Valuation Chaper 6 Ineres Raes and Bond Valuaion Definiion and Descripion of Bonds Long-erm deb-loosely, bonds wih a mauriy of one year or more Shor-erm deb-less han a year o mauriy, also called unfunded deb Bond-sricly

More information

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides 7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion

More information

How Much Can Taxes Help Selfish Routing?

How Much Can Taxes Help Selfish Routing? How Much Can Taxe Help Selfih Rouing? Tim Roughgarden (Cornell) Join wih Richard Cole (NYU) and Yevgeniy Dodi (NYU) Selfih Rouing a direced graph G = (V,E) a ource and a deinaion one uni of raffic from

More information

Transient Analysis of First Order RC and RL circuits

Transient Analysis of First Order RC and RL circuits Transien Analysis of Firs Order and iruis The irui shown on Figure 1 wih he swih open is haraerized by a pariular operaing ondiion. Sine he swih is open, no urren flows in he irui (i=0) and v=0. The volage

More information

Capital budgeting techniques

Capital budgeting techniques Capial budgeing echniques A reading prepared by Pamela Peerson Drake O U T L I N E 1. Inroducion 2. Evaluaion echniques 3. Comparing echniques 4. Capial budgeing in pracice 5. Summary 1. Inroducion The

More information

Module 3 Design for Strength. Version 2 ME, IIT Kharagpur

Module 3 Design for Strength. Version 2 ME, IIT Kharagpur Module 3 Design for Srengh Lesson 2 Sress Concenraion Insrucional Objecives A he end of his lesson, he sudens should be able o undersand Sress concenraion and he facors responsible. Deerminaion of sress

More information

Hedging with Forwards and Futures

Hedging with Forwards and Futures Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures

More information

2.4 Network flows. Many direct and indirect applications telecommunication transportation (public, freight, railway, air, ) logistics

2.4 Network flows. Many direct and indirect applications telecommunication transportation (public, freight, railway, air, ) logistics .4 Nework flow Problem involving he diribuion of a given produc (e.g., waer, ga, daa, ) from a e of producion locaion o a e of uer o a o opimize a given objecive funcion (e.g., amoun of produc, co,...).

More information

PRESSURE BUILDUP. Figure 1: Schematic of an ideal buildup test

PRESSURE BUILDUP. Figure 1: Schematic of an ideal buildup test Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics PRESSURE BUILDUP I is difficul o kee he rae consan in a roducing well. This is no an issue in a buildu es since he well is closed.

More information

Simulation of the motion of a sphere through a viscous fluid

Simulation of the motion of a sphere through a viscous fluid ENSEÑANZA REVISTA MEXICANA DE FÍSICA 49 () 166 174 ABRIL 003 Simulaion of he moion of a sphere hrough a viscous fluid R.M. Valladares a, P. Goldsein b, C. Sern c, and A. Calles d Deparameno de Física,

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

SkySails Tethered Kites for Ship Propulsion and Power Generation: Modeling and System Identification. Michael Erhard, SkySails GmbH, Hamburg, Germany

SkySails Tethered Kites for Ship Propulsion and Power Generation: Modeling and System Identification. Michael Erhard, SkySails GmbH, Hamburg, Germany SkySails Tehered Kies for Ship Propulsion and Power Generaion: Modeling and Sysem Idenificaion Michael Erhard, SkySails GmbH, Hamburg, Germany Conens Inroducion SkySails Marine and Power Simple Model Sensors

More information

UNIT 3 POWER TRANSMISSION DEVICES

UNIT 3 POWER TRANSMISSION DEVICES UNI 3 POWER RANSMISSION DEVIES Power ransmission Devices Srucure 3. Inroducion Objecives 3. Power ransmission Devices 3.. Bels 3.. hain 3..3 Gears 3.3 ransmission Screw 3.4 Power ransmission by Bels 3.4.

More information

C The Fast-Dealing Property Trading Game C

C The Fast-Dealing Property Trading Game C AGES 8+ C The Fas-Dealing Propery Trading Game C Y riginal MNPLY Game Rules plus Special Rules for his Ediion. CNTENTS Gameboard, 6 okens, 28 Tile Deed cards, 6 U.N.I.T Cards, 6 Gallifrey Cards, pack of

More information

Mortality Variance of the Present Value (PV) of Future Annuity Payments

Mortality Variance of the Present Value (PV) of Future Annuity Payments Morali Variance of he Presen Value (PV) of Fuure Annui Pamens Frank Y. Kang, Ph.D. Research Anals a Frank Russell Compan Absrac The variance of he presen value of fuure annui pamens plas an imporan role

More information

Markit Excess Return Credit Indices Guide for price based indices

Markit Excess Return Credit Indices Guide for price based indices Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semi-annual

More information