Answer: 1) Force 2) Velocity and 6) Acceleration are vectors. All other quantities do not have direction and they are scalars.

Size: px
Start display at page:

Download "Answer: 1) Force 2) Velocity and 6) Acceleration are vectors. All other quantities do not have direction and they are scalars."

Transcription

1 H3 ecrs and prjecile min Prblem : Answer he fllwin quesin cncernin ecrs. Par (a) Frm he ien lis chse all ha are eamples f ecrs. ) Frce. ) Speed. 3) elci. 4) Mass. 5) lume. 6) Accelerain. 7) Temperaure. Answer: ) Frce ) elci and 6) Accelerain are ecrs. All her quaniies d n hae direcin and he are scalars.

2 Prblem : Cnsider he w ecrs A and B. Yu knw he maniudes f hese ecrs ( m and m respeciel), bu u d n knw anhin abu heir direcins. Par (a) If a ecr C is defined be he sum f hese w ecrs (i.e. C = A + B) which f he fllwin are rue abu he maniude f C? Chse all ha appl. MulipleSelec : ) C min = 9 ) C min = ( + ).5 3) C ma = 4) C min cann be deermined. 5) C ma = 6) C ma = ( + ).5 7) C min = 8) C min = -9 ) Crrec. C is minimum when B A ) rn. Cann be rih if ) is crrec. 3) Crrec. C is maimum when B A 4) rn. Cann be rih if ) is crrec. 5) rn. Cann be rih if 3) is crrec. 6) rn. Cann be rih if 3) is crrec. 7) rn. Cann be rih if ) is crrec. 8) rn. Cann be rih if ) is crrec.

3 Prblem 3: ecr A has a ien maniude f A and pins due Eas. ecr B f unknwn maniude pins direcl Nrh. The sum A + B makes an anle f θ derees Nrh f Eas. Par (a) rie an epressin fr he maniude f ecr B in erms f he maniude f A, A, and he anle θ, u an required rinmeric funcins. Par (b) ha is he numerical alue fr he maniude f he difference f ecrs A and B, A - B? Par (c) ha is he numerical alue fr he maniude f he sum f ecrs A and B, A + B? Numeric : A numeric alue is epeced and n an epressin. Sluin: (a) B A B an A B A an (b) I redraw he fiure fr clari: P A B A + B Q B B O A A

4 A A - B Bu PO is cnruen QO (SAS), s A A A - B A - B (c) A+B A A A B A B A

5 Prblem 4: Find he fllwin fr pah B in he Fiure shwn where lenh f ne blck is l = L m. Par (a) Find he al disance raeled in km. Par (b) Find he maniude f he displacemen in meers. Par (c) Find he anle, in derees, f he direcin f he displacemen measured Nrh f Eas. Sluin: (a) Pah B: 4 blcks eas, 3 blcks nrh, and 3 blcks wes, al disance raeled = = blcks. al disance raeled = L meers = L/ = L/ km (b) 3L r r 3L 3L 4L 3L=L 4L r (3L) (L) L L 3.6L (c) 3L r r 3L 3L 4L 3L=L 4L an 3L L 3 an

6 The direcin f he displacemen is 7.57 Nrh f Eas.

7 Prblem 5: The fiure depics he sum f w elciies. Par (a) Find he cmpnen f aln he ais in m/s. Par (b) Find he cmpnen f aln he ais in m/s. Sluin: (a) T 6.7 ( m/s.5 ) (b) T 6.7 ( m/s.5 )

8 Prblem 5: The fiure depics he sum f w elciies. Par (a) Find he cmpnen f aln an ais raed 3 cunerclckwise relaie hse in he Fiure. Par (b) Find he cmpnen f aln a ais raed 3 cunerclckwise relaie hse in he Fiure. Sluin: ' Le us d sme simple emer firs. M firs al is fiure u he anle beween B and he ais. ' O 3 D +3 = = 49 = 9 (a) T ' m/s (b) T ' m/s

9 Prblem 7: A farmer wans fence ff his fur-sided pl f fla land. He measures he firs hree sides, shwn as A, B, and C in he fiure, where A = A km, B = B km, and C = C km and hen crrecl calculaes he lenh and rienain f he furh side D. Par (a) ha is he lenh f he ecr D in kilmeers? Par (b) ha is he rienain f he ecr D, in derees f S? (a) Ne ha A B C D D A B C D D A A B A 7.5 B C C ( B6 ) ( C9 ).994A (.756B) (.9455C).994A.756B.9455C ( A 7.5 ) (B6 ) (C 9 ) (.35A) (.963B) (.356C).35A.963B.356C D D D (.994A.756B.9455C) (.35A.963B.356C)

10 .356C.963B.35A.9455C.756B.994A an D D an D D Adjacen side Oppsie side an - - (b)

11 Prblem 8: A ship ses sail frm erdam, The Neherlands, headin due nrh a S m/s relaie he waer. The lcal cean curren is m/s in a direcin nrh f eas. Par (a) ha is he maniude f he elci f he ship relaie he Earh in m/s? Par (b) ha is he anle f he elci f he ship relaie he Earh in derees N f E? Sluin N S S E elci f ship relaie waer elci f ship - elci f waer S S The prblem is askin fr S S S (a) N S S E S S S S S S S S S ( S ) ( S ( ) S ( S S ) ) ( S S ) ( ) S S S S

12 an an ) ( ) ( S - S S S S S S S S S S S S S (b) S S E N

13 Prblem 9: An ice hcke plaer is min a plaer m/s when he his he puck ward he al. The speed f he puck relaie he plaer is puck m/s. The line beween he cener f he al and he plaer makes a 9. anle relaie his pah as shwn in he fiure. Par (a) ha anle mus he puck s elci make relaie he plaer (in his frame f reference) hi he cener f he al in derees? Sluin: The ien fiure and he wa i names ariables is acuall kind f cnfu, s le me clarif here: plaer is he elci f plaer relaie he Earh, n cnfusin here. puck is acuall he elci f he puck relaie he plaer, s be careful here. Acuall i is clear if u read he prblem e carefull. is he elci f he puck relaie he Earh. S elci f puck relaie plaer = elci f puck elci f plaer will ie puck = plaer. puck puck puck puck puck puck puck () /() an an puck puck plaer plaer plaer plaer plaer plaer plaer plaer ( ( () and () and plaer plaer ) plaer )

14 Prblem : A famus lfer srikes a lf ball n he rund, iin i an iniial elci = i + j. Assume he ball mes wihu air resisance and is min is described u a Caresian crdinae ssem wih is riin lcaed a he ballʼs iniial psiin. Par (a) Deermine he maimum heih abe rund, hma in meers, aained b he lf ball. Par (b) Epress he al hriznal disance, ma, he ball raels when i reurns rund leel in erms f,, and. Par (c) Ealuae he al hriznal disance, ma in meers, he ball raels when i reurns rund leel. Sluin: Equains f min : i i a a i i i i () () (3) (4) (a) A hihes pin (4) -

15 Subsiue his in (3) hihes (b) and (c) : hen he lf ball reurns rund, (3) crrespnds he launchin pin, s he ball will hill he rund aain when Subsiue his in () ( r r rane )

16 Prblem : A quarerback hrws a fball wih an iniial elci a an anle θ abe hriznal. Assume he ball leaes he quarerback s hand a rund leel and mes wihu air resisance. All prins f his prblem will prduce alebraic epressins in erms f, θ, and. Le he riin f he Caresian crdinae ssem be he ballʼs iniial psiin. Par (a) rie an epressin fr he maniude f he fball s iniial erical elci. Par (b) Find an epressin fr he maniude f he fball s iniial hriznal elci. Par (c) rie an epressin fr he al ime, al, he fball is abe he rund. Sluin: Equains f min : i i a a (a) (b) i (c) hen he fball reurns rund, (3) al i i i - ( ime fr he fball abe rund ) r r r al () () (3) (4)

17 Prblem : An arrw is fired upward wih an iniial elci a an anle θ abe hriznal. Assume he arrw mes wihu air resisance. Use a Caresian crdinae ssem wih he riin a he arrwʼs iniial psiin analze he arrwʼs min. Par (a) Sme ime laer he arrw makes an anle f θ derees wih respec he hriznal. rie an epressin fr he ime,, ha passes beween when he arrw was fired and his laer pin. Sluin: Equains f min : i i a a If he elci a he pin where he arrw makes an anle wih respec rund is. i i i and - () (4) - - i () () (3) (4)

18 ) - ( ) - ( \

19 Prblem 3: A suden hrws a sne frm he p f a cliff a a disance d m abe a hriznal plane wih iniial elci m/s a an anle θ belw hriznal. The sne mes wihu air resisance; use a Caresian crdinae ssem wih he riin a he sneʼs iniial psiin. Par (a) ih wha speed, f in m/s, des he sne srike he rund? Par (b) If he sne had been hrwn frm he cliffp in he same manner bu upward insead f dwnward, wuld is impac elci be differen? Sluin: O = d (a) Equains f min : i i a - a - - i hen he sne his he bm f he cliff, (3) i i - d - d i - ( ) ( ) - d ( ) d - d 4(-d) () () (3) (4)

20 d, s has w rs, ne psiie and ne neaie. e will ake he psiie r. O = d Neaie r crrespnds his pin Psiie r crrespnds his pin (4) - f f - - (- - d d d) f - - d) () f f - d f f f ( ) (- d) d d ( )

21 (b) If he sne s hrwn in similar manner bu upward in he f dwnward, his will nl affec he f sme erms in he equains f min. Equain (3) and (4) has be rewrien as: i i a a - i New (3) - d ( ) - d Takin psiie, New (4) f ( ) d - 4(-d) f f d - ( d (3) (4) d ) S we hae he same f as if he sne is hrwn dwnward. e can cnclude ha he impac elci shuld be he same.

22 Prblem 4: A ball is kicked wih an iniial elci f m/s in he hriznal direcin and m/s in he erical direcin. Par (a) A wha speed des he ball hi he rund in m/s? Par (b) Fr hw ln des he ball remain in he air in secnds? Par (c) ha maimum heih is aained b he ball in meers? ` Sluin Equains f min : i i a a Answer par (b) firs : (b) (3) i i i i hen he fball reurns crrespnds he launchin pin, s he ball will hill he rund aain when The ball will sa abe rund fr a Nw par (a) : (a) Subsiue - ( in (3) - rund, - perid f ) r r () () (3) (4) (make sense?)

23 () he ball will hi he rund wih a speed (- ) (c) A hihes pin (4) - Subsiue his in (3) hihes

24 Prblem 5: A fball plaer puns he ball a a anle. ihu an effec frm he wind, he ball wuld rael m hriznall. Par (a) ha is he iniial speed f he ball in m/s? Par (b) hen he ball is near is maimum heih i eperiences a brief us f wind ha reduces is hriznal elci b m/s. ha disance des he ball rael hriznall? Sluin Equains f () i i i i (a) hen he ball his (3) min : i i a a - he rund aain, ( crrespnds he launchin pin, s he ball will hi he rund aain when (, 9 ) ) r ( ) () () (3) r (4)

25 (b) A hihes pin (4) - Subsiue his in (3) hihes 4 (, 9, frm par (a)) edefine crdinaes and rese ime afer reachin he hihes pin: 4 / Equains f min : i i i i i - i (a) hen he ball his a - (3) 4 a ( - ) 4 he rund aain, (5) (6) (7) (8)

26 ) - an ( ' disance raelled b he fball Hriznal ) - an ( ) - ( ) - ( ) - ( ) - ( ' Bu frm par (a) ) - ( ) - ( (5) 4

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

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

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

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

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

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

Lecture #13. Mutual Inductance

Lecture #13. Mutual Inductance ecure #3 ANNOUNCEMENTS Graded HW can be picked up in 78 Cry OUTNE Muual inducance Firs-rder circuis Naural respnse f an circui eang Chaper 6.4, Chaper 7. ecure 3, Slide Muual nducance Muual inducance ccurs

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

Vectors and vector calculus

Vectors and vector calculus Cprigh iuecm 6 Free dwnld & prin frm wwwiuecm D n reprduce her mens Vecrs nd ecr clculus Vecrs in w nd hree dimensins Free ecrs: A ecr is free if i is cnsidered e he sme ecr under rnslin PQ is free ecr

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

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

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

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

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

1 CHAPTER 3 TEMPERATURE

1 CHAPTER 3 TEMPERATURE 1 CHAPTER 3 TEMPERATURE 3.1 Inrducin During ur sudies f hea and hermdynamics, we shall cme acrss a number f simple, easy-undersand erms such as enrpy, enhalpy, Gibbs free energy, chemical penial and fugaciy,

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

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

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

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 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

2.5 Life tables, force of mortality and standard life insurance products

2.5 Life tables, force of mortality and standard life insurance products Soluions 5 BS4a Acuarial Science Oford MT 212 33 2.5 Life ables, force of moraliy and sandard life insurance producs 1. (i) n m q represens he probabiliy of deah of a life currenly aged beween ages + n

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

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

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

I. Basic Concepts (Ch. 1-4)

I. Basic Concepts (Ch. 1-4) (Ch. 1-4) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing

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

FOUNDATION SETTLEMENT

FOUNDATION SETTLEMENT FOUNDATION ETTLEMENT Dr.. K. Prasad Prfessr f Civil Engineering. J. Cllege f Engineering, Mysre 8.0 yllabus 1. elemen Analysis, Daa fr selemen analysis. Cmpuain f selemen 3. Cncep, Immediae, Cnslidain

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

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

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

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

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

Oblique incidence: Interface between dielectric media

Oblique incidence: Interface between dielectric media lecrmagnec Felds Oblque ncdence: Inerface beween delecrc meda Cnsder a planar nerface beween w delecrc meda. A plane wave s ncden a an angle frm medum. The nerface plane defnes he bundary beween he meda.

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

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

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

Work, Energy, and Power. AP Physics C

Work, Energy, and Power. AP Physics C rk, Energ, and Pwer AP Phsics C There are man different TYPES f Energ. Energ is expressed in JOULES (J) 4.19 J 1 calrie Energ can be expressed mre specificall b using the term ORK() rk The Scalar Dt Prduct

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

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

WHAT ARE OPTION CONTRACTS?

WHAT ARE OPTION CONTRACTS? WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be

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

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

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

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

Section 24 exemption application

Section 24 exemption application Fr ffice use nly Auhrisain number: Secin 24 exempin applicain This frm is fr persns applying fr an exempin under secin 24 f he Plumbers, Gasfiers, and Drainlayers Ac 2006. This exempin auhrises a persn

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

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

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

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

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

SHB Gas Oil. Index Rules v1.3 Version as of 1 January 2013

SHB Gas Oil. Index Rules v1.3 Version as of 1 January 2013 SHB Gas Oil Index Rules v1.3 Version as of 1 January 2013 1. Index Descripions The SHB Gasoil index (he Index ) measures he reurn from changes in he price of fuures conracs, which are rolled on a regular

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

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

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

Analysis of tax effects on consolidated household/government debts of a nation in a monetary union under classical dichotomy

Analysis of tax effects on consolidated household/government debts of a nation in a monetary union under classical dichotomy MPRA Munich Personal RePEc Archive Analysis of ax effecs on consolidaed household/governmen debs of a naion in a moneary union under classical dichoomy Minseong Kim 8 April 016 Online a hps://mpra.ub.uni-muenchen.de/71016/

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

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

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

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

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high

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

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

Chapter 11. Industry Productivity Measures IN THIS CHAPTER. Background Studies of output per hour in individual industries have

Chapter 11. Industry Productivity Measures IN THIS CHAPTER. Background Studies of output per hour in individual industries have Chaper. Indusry Prduciviy Measures Backgrund Sudies f upu per hur in individual indusries have been par f he U.S. Bureau f Labr Saisics (BLS) prgram since he 800s. Prmped by cngressinal cncern ha human

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

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

Chapter 9 Bond Prices and Yield

Chapter 9 Bond Prices and Yield Chaper 9 Bond Prices and Yield Deb Classes: Paymen ype A securiy obligaing issuer o pay ineress and principal o he holder on specified daes, Coupon rae or ineres rae, e.g. 4%, 5 3/4%, ec. Face, par value

More information

Education & Human Resource Development

Education & Human Resource Development Educaion & Human Resource Developmen New Research Adminisraion Srucure Rerea June 23 & 24, 2006 Where is he Caribbean in Relaion o Oher Counries? Office of he Vice Presiden for Research and Compliance

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 Note on the Real Exchange Rate

Lecture Note on the Real Exchange Rate Lecure Noe on he Real Exchange Rae Barry W. Ickes Fall 2004 0.1 Inroducion The real exchange rae is he criical variable (along wih he rae of ineres) in deermining he capial accoun. As we shall see, his

More information

Regions File Transmission

Regions File Transmission Regins File Transmissin Getting Started with FTPS Regins Bank Member FDIC Revised 022113 It s time t expect mre. Table f Cntents Getting Started with FTPS Setting Up FTPS Cnnectin in FTP Client 3 4 9 Regins

More information

NASDAQ-100 Futures Index SM Methodology

NASDAQ-100 Futures Index SM Methodology NASDAQ-100 Fuures Index SM Mehodology Index Descripion The NASDAQ-100 Fuures Index (The Fuures Index ) is designed o rack he performance of a hypoheical porfolio holding he CME NASDAQ-100 E-mini Index

More information

Credit Index Options: the no-armageddon pricing measure and the role of correlation after the subprime crisis

Credit Index Options: the no-armageddon pricing measure and the role of correlation after the subprime crisis Second Conference on The Mahemaics of Credi Risk, Princeon May 23-24, 2008 Credi Index Opions: he no-armageddon pricing measure and he role of correlaion afer he subprime crisis Damiano Brigo - Join work

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

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

Writing a Compare/Contrast Essay

Writing a Compare/Contrast Essay Writing a Cmpare/Cntrast Essay As always, the instructr and the assignment sheet prvide the definitive expectatins and requirements fr any essay. Here is sme general infrmatin abut the rganizatin fr this

More information

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999 TSG-RAN Working Group 1 (Radio Layer 1) meeing #3 Nynashamn, Sweden 22 nd 26 h March 1999 RAN TSGW1#3(99)196 Agenda Iem: 9.1 Source: Tile: Documen for: Moorola Macro-diversiy for he PRACH Discussion/Decision

More information

12. TESTING OF CEMENT PART 1.

12. TESTING OF CEMENT PART 1. Chaper 12-Tesing of Cemen Par 1 12. TESTING OF CEMENT PART 1. 12.1 Densiy The densiy is he fundamenal physical characerisic of he maerial. Densiy is defined by mass of a uni volume of a maerial subsance,

More information

How much life insurance do I need? Wrong question!

How much life insurance do I need? Wrong question! Hw much life insurance d I need? Wrng questin! We are ften asked this questin r sme variatin f it. We believe it is NOT the right questin t ask. What yu REALLY need is mney, cash. S the questin shuld be

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

Nikkei Stock Average Volatility Index Real-time Version Index Guidebook

Nikkei Stock Average Volatility Index Real-time Version Index Guidebook Nikkei Sock Average Volailiy Index Real-ime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and

More information

Space Exploration Classroom Activity

Space Exploration Classroom Activity Space Explratin Classrm Activity The Classrm Activity intrduces students t the cntext f a perfrmance task, s they are nt disadvantaged in demnstrating the skills the task intends t assess. Cntextual elements

More information

Astable multivibrator using the 555 IC.(10)

Astable multivibrator using the 555 IC.(10) Visi hp://elecronicsclub.cjb.ne for more resources THE 555 IC TIMER The 555 IC TIMER.(2) Monosable mulivibraor using he 555 IC imer...() Design Example 1 wih Mulisim 2001 ools and graphs..(8) Lile descripion

More information

COMPUTATION OF CENTILES AND Z-SCORES FOR HEIGHT-FOR-AGE, WEIGHT-FOR-AGE AND BMI-FOR-AGE

COMPUTATION OF CENTILES AND Z-SCORES FOR HEIGHT-FOR-AGE, WEIGHT-FOR-AGE AND BMI-FOR-AGE COMPUTATION OF CENTILES AND Z-SCORES FOR HEIGHT-FOR-AGE, WEIGHT-FOR-AGE AND BMI-FOR-AGE The mehod used o consruc he 2007 WHO references relied on GAMLSS wih he Box-Cox power exponenial disribuion (Rigby

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

E0 370 Statistical Learning Theory Lecture 20 (Nov 17, 2011)

E0 370 Statistical Learning Theory Lecture 20 (Nov 17, 2011) E0 370 Saisical Learning Theory Lecure 0 (ov 7, 0 Online Learning from Expers: Weighed Majoriy and Hedge Lecurer: Shivani Agarwal Scribe: Saradha R Inroducion In his lecure, we will look a he problem of

More information

Student Web Time Entry Guide

Student Web Time Entry Guide Student Web Time Entry Guide Updated July 6, 2015 TABLE OF CONTENTS TABLE OF CONTENTS... 1 GETTING STARTED... 2 HOW TO ACCESS BANNER ONLINE... 2 HOW TO ENTER CURRENT TIMESHEETS... 2 HOW TO ENTER PREVIOUS

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

Data Validation and Iteration

Data Validation and Iteration Financial Mdeling Data Validatin and Iteratin As analysts are bmbarded with a lt ff data, ne shuld be able t check data veracity. This is where the data validatin functins cme in handy. Few excel functins

More information

Fakultet for informasjonsteknologi, Institutt for matematiske fag

Fakultet for informasjonsteknologi, Institutt for matematiske fag Page 1 of 5 NTNU Noregs eknisk-naurviskaplege universie Fakule for informasjonseknologi, maemaikk og elekroeknikk Insiu for maemaiske fag - English Conac during exam: John Tyssedal 73593534/41645376 Exam

More information

DECOMPOSING THE BID-ASK SPREAD OF STOCK OPTIONS: A TRADE AND RISK INDICATOR MODEL

DECOMPOSING THE BID-ASK SPREAD OF STOCK OPTIONS: A TRADE AND RISK INDICATOR MODEL DECOMPOSING THE BID-ASK SPREAD OF STOCK OPTIONS: A TRADE AND RISK INDICATOR MODEL David Michayluk Schl f Finance and Ecnmics Universiy f Technlgy, Sydney Ausralia Phne: 61--9514-7761 Fax: 61--9514-7711

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

Master of Social Work Feasibility Survey for Prospective Students. For Online/Hybrid Program

Master of Social Work Feasibility Survey for Prospective Students. For Online/Hybrid Program Master f Scial Wrk Feasibility Survey fr Prspective Students Fr Online/Hybrid Prgram Dear Survey Participant, The Central Regin Partnership f Mental Health Directrs is interested in funding an Online/Hybrid

More information

On alternative methods of determining Radius of Curvature using Newton s Rings set up

On alternative methods of determining Radius of Curvature using Newton s Rings set up Inernaional Leers of Chemisry, Physics and Asronomy Online: 0-03-5 ISSN: 99-3843, Vol. 48, pp 7-31 doi:10.1805/www.scipress.com/ilcpa.48.7 0 SciPress Ld., Swizerland On alernaive mehods of deermining Radius

More information

Backward Design Lesson Planning. How do I determine and write lesson objectives? (identifying desired results)

Backward Design Lesson Planning. How do I determine and write lesson objectives? (identifying desired results) Backward Design Lessn Planning Hw d I determine and write lessn bjectives? (identifying desired results) Intrductin All lessns, regardless f which lessn-planning mdel that yu use, begins with identifying

More information

The ad hoc reporting feature provides a user the ability to generate reports on many of the data items contained in the categories.

The ad hoc reporting feature provides a user the ability to generate reports on many of the data items contained in the categories. 11 This chapter includes infrmatin regarding custmized reprts that users can create using data entered int the CA prgram, including: Explanatin f Accessing List Screen Creating a New Ad Hc Reprt Running

More information

Description of the CBOE S&P 500 BuyWrite Index (BXM SM )

Description of the CBOE S&P 500 BuyWrite Index (BXM SM ) Descripion of he CBOE S&P 500 BuyWrie Index (BXM SM ) Inroducion. The CBOE S&P 500 BuyWrie Index (BXM) is a benchmark index designed o rack he performance of a hypoheical buy-wrie sraegy on he S&P 500

More information

GoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results:

GoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results: For more informaion on geneics and on Rheumaoid Arhriis: Published work referred o in he resuls: The geneics revoluion and he assaul on rheumaoid arhriis. A review by Michael Seldin, Crisopher Amos, Ryk

More information

Optimal Investment and Consumption Decision of Family with Life Insurance

Optimal Investment and Consumption Decision of Family with Life Insurance Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker

More information