Name: Per: L o s A l o s H i g h S c h o o l Phsics Uni Workbook Two Dimensional Kinemaics Mr. Randall 1968 - Presen adam.randall@mla.ne www.laphsics.com a o 1 a o o ) ( o o a o o ) ( 1 1 a o g o 1 g o o ) ( o o g o o ) ( 1 1 g o ) ( 1 ag V o V V Y V X ag V a ag
Uni - Two Dimensional Kinemaics Objecies & Assignmens B he end of his uni, ou will be able o: 1. Relae he direcion and magniude of posiion, eloci and acceleraion ecors o he moion of objecs in freefall.. Creae picorial and phsical models for soling moion problems. 3. Skech qualiaie graphs of posiion, eloci and acceleraion s. ime for objecs moing in wo dimensions. 4. Calculae he displacemen of an objec from he area under a eloci s. ime graph. 5. Calculae he change in eloci of an objec from he area under an acceleraion s. ime graph. 6. Calculae he displacemen and eloci of an objec undergoing consan acceleraion. 7. Predic and calculae displacemen, eloci and ime for objecs free falling in wo dimensions. 8. Define he magniude of he acceleraion due o grai and deermine he sign of he acceleraion relaie o he chosen coordinae ssem. 9. Use 5 kinemaics equaions o sole problems inoling objecs moing a consan acceleraion and inoling objecs in free fall. 10. Measure, record and analze moion in wo dimensions using sop moion image analsis and spreadshees. 11. Sole some reall cool projecile moion problems. 1. Decompose wo dimensional eloci ecors using Sine & Cosine. 13. Compose wo dimensional eloci ecors using he heorem of Phagoras and he inerse Tangen.
Two Dimensional Kinemaics - Assignmen Shee Dae # Assignmen Tile Due Dae 1 Read Chapers 3.1 3.3 Workbook Problems #:, 4 Frida 10/3 Take Home D Kinemaics Quiz Monda 10/6 3 4 5 6 7 8 Take Home Quiz Frida, 10/3/014 Quiz Frida, 10/10/014 Uni Tes Frida, 10/17/014 3
Los Alos High School Phsics Two Dimensional Kinemaics Workbook Problems 1. Consider a Unied Saes Coas Guard plane fling a rescue mission 300 Km Wes of he Farallon Islands. The mission requires he plane s crew o delier a 50 kg package of emergenc supplies o he crew of a sranded sail boa waiing for repair. Your job is o deermine how far before he boa he package should be released such ha he package lands righ on he boa s deck. The plane will be fling a an aliude of 15 m aboe he boa s deck and raeling wih a consan eloci of 86.0 m/s @ 0.00. A. Predic and calculae he ime i will ake for he package o free-fall o he boa s deck. B. Predic and calculae he horizonal displacemen, or he range, of he package while in free-fall. C. Skech a diagram describing where he plane should be when he package is released such ha he package lands righ on he boa s deck? D. Predic he final speed of he package, jus before i srikes he boa s deck. E. Skech posiion, eloci and acceleraion graphs for he package during freefall in each dimension. F. Wha do ou hink abou he rescue mission s plan? Would ou change i? Briefl eplain. 4
Los Alos High School Phsics Two Dimensional Kinemaics Workbook Problems. Consider Los Angeles Dodger, Hanle Ramirez, o hae jus hi a homerun agains he Gians a he AT&T Park in San Francisco. A Gians fan in he lef field bleachers caches he ball and rejecs he homerun b hrowing he ball back ono he plaing field. The ball is hrown wih an iniial eloci of 4.0 m/s @ 0.00. If he iniial heigh of he ball is 45.0 m aboe he plaing field: A. Predic and calculae he ime i akes for he ball o free-fall o he plaing field. B. Predic and calculae he Range (horizonal displacemen) of he ball. C. Predic and calculae he speed of he ball jus before i srikes he plaing field. D. Skech posiion, eloci and acceleraion graphs for he ball s free-fall in boh dimensions. 5
Los Alos High School Phsics Two Dimensional Kinemaics Workbook Problems 3. Consider a golf ball launched wih an iniial eloci of 48.0 m/s @ 45.0. You obsere he ball freefalling aboe he fairwa. Suddenl, he insan afer he ball reaches he ape (ape highes erical posiion) of i s parabolic rajecor, i plugs ino a gian cacus a he edge of a all cliff high aboe where he ball was launched. A. Predic and calculae he ime needed for he golf ball o reach he ape. B. Predic and calculae he golf ball s range (horizonal displacemen during freefall.) C. Predic and calculae he golf ball s maimum heigh. D. Predic and calculae he golf ball s eloci a he ape, jus before sriking he cacus. E. Sae he golf ball s acceleraion a he ape, jus before sriking he cacus. F. Skech posiion, eloci and acceleraion graphs for he golf ball o he ape. 6
Los Alos High School Phsics Two Dimensional Kinemaics Workbook Problems 4. Consider a soccer plaer kicking a ball agains a wall. Suddenl, he plaer kicks he ball from ground leel wih an iniial eloci of 8.0 m/s @ 35.0. The ball passes hrough a window in he wall as i reaches is maimum heigh. Assume he ball is in free-fall. A. Predic and calculae he ime needed for he ball o reach he ape. B. Predic and calculae he ball s range (horizonal displacemen during freefall.) C. Predic and calculae he ball s maimum heigh. D. Predic and calculae he ball s eloci a is ape. E. Sae he ball s acceleraion a he ape, jus before passing hrough he window. F. Skech posiion, eloci and acceleraion graphs for he ball o he ape. 7
Los Alos High School Phsics Two Dimensional Kinemaics Workbook Problems 5. A fooball quarerback hrows a pass o a receier, who caches i a he same heigh as he pass is hrown. The iniial eloci of he ball is.5 m/s, a an angle of 63.0 aboe he horizonal. Assume he ball is in free-fall. A. Predic and calculae he oal ime he ball is in freefall. B. Predic and calculae he ball s eloci a he ape of is parabolic rajecor. C. Calculae he final eloci jus before he receier caches he ball. D. Calculae he fooball s range. E. Sae he acceleraion of he ball 1.0s before i is caugh. F. Skech posiion, eloci and acceleraion graphs for he fooball during free-fall in wo dimensions. 8
Los Alos High School Phsics Two Dimensional Kinemaics Workbook Problems 6. An Olmpic long jumper leaes he ground wih an iniial eloci of 11.0 m/s a 40.0 o aboe he horizonal. The jumper lands a he same erical posiion as he jumped from. Assume he jump o be in free-fall. A. Predic and calculae he long jumper s maimum heigh. B. Predic and calculae he long jumper s eloci a he ape. C. Predic and calculae he jumper s range. D. Predic and calculae he final eloci jus before she his he ground. E. Sae her acceleraion 0.301s afer she jumps. F. Skech posiion, eloci and acceleraion graphs for he jumper during he enire freefall. 9
Los Alos High School Phsics Two Dimensional Kinemaics Workbook Problems 7. Derie a funcion for he range of an objec in ground o ground free-fall, wih a consan launch speed, as a funcion of launch angle and show ha: is alid. V X ( θ ) Sin(θ ) g A. Derie an equaion predicing he ime in freefall. B. Subsiue he smbolic epression for ime ino he big dog displacemen equaion. C. Use he rigonomeric ideni Sin(θ)SinθCosθ D. Skech a graph of Range as a funcion of Launch Angle beween 0 and 90 degrees. E. Show b smmer on he graph how smmerical angles achiee equal ranges for consan launch speeds. 10
Los Alos High School Phsics Two Dimensional Kinemaics Workbook Problems 8. Consider Ror Mcllro driing a golf ball from a plaeau 65.0 meers aboe he fairwa. If he ball s iniial eloci is measured o be 84.5 m/s @ 37.0, deermine he following kinemaic quaniies assuming free-fall condiions: A. Deermine he ball s heigh a he ape of is parabolic rajecor, measured from he fairwa. B. Deermine he ball s eloci a he ape. C. Deermine he ball s oal ime in freefall. D. Deermine he ball s freefall range. F. Skech posiion, eloci and acceleraion graphs for he ball during he enire freefall. 11
Los Alos High School Phsics Two Dimensional Kinemaics Workbook Problems 9. Consider Yoann Lerou, an inernaional Parkour ahlee, jumping from ground leel o a handrail 1.0 m high. Yoann s iniial freefall eloci is measured o be 8.60 m/s @ 79.4. Yoann lands on he rail afer passing hrough he ape of his parabolic rajecor. Deermine he following kinemaic quaniies: A. Deermine Yoann s heigh a he ape of his parabolic rajecor, measured from he ground leel. B. Deermine Yoann s eloci a he ape. C. Deermine Yoann s oal ime in freefall. D. Deermine Yoann s freefall range. F. Skech posiion, eloci and acceleraion graphs for Yoann during he enire freefall. 1