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