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Unformatted text preview: as tel-interest a HtHEMATICE tH TWD DIMENSIONS the nther tree. Then. he jumps back tn the First tree. landing an it at a spnt that is L? m abnve the grnund. Finally. he leaps hack tn the ether tree. nnw landing at a spnt that is 2.5 m abnve the grnund. What is tlte magnitude at the squirrel‘s displacement‘.l 2. at jetliner is mnving at a speed nt' 245 hits. The vertical cnmpn- nent cf the plancls veln-city is we mi's. Determine the magnitude nf the hnrixnntal cnmpnnent nf the plane‘s velncity. 3. In a fnntball game a kicker attempts a field gas]. The ball remains in cnntact with the kickerls fnnt fer {Lllfitl a. during which time it ex- periences an acceleratintt ni' 34D ITU‘SI. The hall is launched at an an- gle nf 51“ abnve the grnund. Determine the hnrisnntal and vertical cnmpnnents til“ the launch velncity. 4. at metenrnid is speeding thrnugh the atmnsphere. traveling east at [3.3 ['1me while descending at a rate at" l [.5 kntis. What is its speed. in kmt's‘l 5. cent at radar antenna is tracking a satellite nrbiting the earth. tit a certain time. the radar screen shnws the satellite in be In: km away. The radar antenna is pninting upward at an angle nf 62.3” item the grnund. Find the .r and y cnmpnnents [in km] nf the pnsitinn vectnr cf the satellite. relative in the antenna. ti. it. mnun taintclimbing expeditinn establishes twn intermediate camps. labeled A and H in the drawing. abnve the base camp. What is the magnitude ctr nf the displacement between camp A and camp ti? 'l'. cent In diving tn a depth at “fill at. an elephant seal alsn mnves 4150 m due east nf his starting pnint. What is the magnitude nf the seal's displacement? 8. @ In a mail. a shnpper rides up an escalatnr between finnrs. At the tap nf the escalatnr. the shnpper turns right and walks 9.0!} m tn a stnre. The magnitude cf the shnpper‘s displacement Irnm the bnt- tnm cf the escalatnr tn the stnre is tall m. The vertical distance be- tween the tinnrs is hilt] m. At what angle is the escalatnr inclined abnve the bnrianntal'l' 9. llfl'l m A skatehnarder. starting t'rnnt rest. rnlls dnwn a llll-m ramp. When she anives at the bnttnm nf the ramp her speed is Tilt] mi's. ta} Determine the magnitude nF her acceleratinn. assumed tn he cnn- stant. [it] If the ramp is inclined at 2533“ with respem tn the grnund. what is the cnmpnnent nf her acceleratien that is parallel tn the grnund‘l * Ill. Interactive snluttnn can at www.wtley.cnmt'cnllegeicutnell presents a mndel fnr snlving this prnblem. The earth mnves arnund the sun in a nearly circular nrbit nf radius thl it: til” tn. During the three summer mnnths {an elapsed time nt‘ 139 K ltl'i sl. the earth mnves nnevt‘nutth cf the distance arnund the sun. {at What is the average speed at the earth? [bl What is the magnitude nt' the average velnc- ityr cf the earth during this pet‘ii'.‘it:l'.JI * 11. Interactive LnarnlnuWare 3.1 at www.wiley.cnrnfcnllcgefcntnell reviews the apprnach taken in prnblems such as this nne. A bird watcher meanders thrnugh the weeds. walking tl.5tl km due east. 0.15 km due snuth. and MS km in a directinn 35.0” nnrth nf west. The time required far this trip is 2.51] h. Determine the magnitude and directinn [relative tn due west} nt‘ the bird watcher’s ta} displace- ment and {It} average velncity. Use kilnmeters and hnurs fnr dis- tance and time. respectively. a: Sectinn 3.2 Equatinns nf Kinematics in Ten Dimenslnns. Sectinn 3.3 Projectile Mntlnn 12.. The punter en a feathall team tries tn kick a fnntball sn that it stays in the air fer a Inng “hang time.“ If the ball is kicked with an initial vein-city at 25.0 mfs at an angle cif fiflfl" abnve the grntintl1 what is the hang time? 13. earn Suppnse that the plane in Example 3 is traveling with hides the hnrixnntal veincity—that is. with a veln-city nf +23t] mils. If all nther factnrs remain the same. determine the time required fer the package in hit the grnund. 14. ® a. puck is mnving nn an air hnckey tahle. Relative tn an x. y cnnrdinate system at time t = {l s. the .r cnmpnnents nt' the puck‘s init tial velncity anti acceleratinn are tin. = + it} mis- and n4. = +21} filial; The y cnmpnnents nt‘ the puck‘s initial velncity and acceleratintt ant em = +21} this and at. = -2.il mi'sE. Find the magnitude and direc- tinn at the packs vclncity at a time ct” t = tljll s. Specify the dime tinn relative tn the +.:r axis. 15. it dnlphin leaps nut cf the water at an angle nt‘ 35” abnve the hut- ixnntal. The bnrixnntal cnmpnnent nf the dnlphin‘s velncity is it? Initi- Find the magnitude cf the vertical cnmpnnent nt" the velncity. In. a skatebnarder shnnts tiff a ramp with a velncity nf an mi's. di't rected at an angle nf 53“ abnve the hnrianntal. The end at the rampi'i LE m abnve the grnund. Let the x axis be parallel tn the grnund. tlti +y directinn be vertically upward. and take as the nrigin the pnint rtj the grnund directly beinw the tnp nf the ramp. {a} Hnw high a t tl'te grnund is the highest pnint that the skatebearder reacl‘et‘i. [b] When the skatehnarder reaches the highest pnint. hnw far is |.'. pnint hnrixnntally t'rnm the end nf the ramp“? ' i‘l'. taint a set-tit ballnnn it titittg straight tip with i spent at an at. A ballast bag is released frnm rest relative tn the ballnnn when ith 9.5 m abnve the grnund. Hnw much time elapses befnre the bag hits the grnundi' ' IE. Ennenpt Elmulatinn 3.1 at www.wiley.cnmt'cnllegeic mi reviews the cnncepts that are impnrtant in this prnblem. A gnifer " parts a speed nf 3&3 mts tn a ball, and it travels the maximum n-.-_ hle distance befnre landing en the green. Thg tee and the green arc -r': the same elevatinn. fa} Hnw much time dnes the ball spend in the ' '5. {hi What is the lnngest hnle in nne that the gnlt‘er can make. if the t-: [a dnes nnt tell when it hits the green? i is. Michael itttattn. fet't‘t'tet'ly at the Chicagtthuut basketball .t'; had snme fanatic Fans. Theyr claimed that he was able tn jump and main in the air fnr twn full sccnnds frnm launch tn landing. Eval i this claim by calculating the maximum height that such ajump u attain. Fnr cnmparisnn. .Inrdan‘s maximum jump height has been timated at ahnut nne meter. Ell. @ it. gnlfer hits a sbnt in a green that is elevated 3.0 m n i;- the pnint where the ball is struck. The ball leaves the club at a cf I41] rats at an angle nf 4fl.ll“ abnve the hnrixnntal. It rises tn' maximum height and then falls dnwn tn the green. Ignnring air ance. find the speed at the ball just bet'nre it lands. | 21. earn it. gnlf ball rnlls eff a hnrienntal clit‘f with an initial t..'- nf l 1.4 mils. The hall Falls a vertical distance at [5.5 at late a lake I"; lnw. {a} Hnw much time dnes the ball spend in the air? {b} ' is the speed it nf the ball just befnre it strikes the water? it space vehicle is ceasting at a cehstant velecity cf 21 .fl W5 in y-directihn relative te a space statien. The pilet ef the vehicle - RC3 (reactien centre! system] dtruster. which fiat-15$ if m 3'3' .- a case stat in the +1 directien. After 45.0 S. the pilet eff the RC3 thruster. After the RC5 thruster is turned eff. find :';';_'s-i'l. magnitude and {It} the directien ef the vehicle’s velecin - tn the space statien. Express the directien as an angle meas— tlte + y directien. As preparatien fer this preh- I{flenccptttal Example lfi. ,dt'ewing shews twe planes each _ I __ drep an empty fuel tank. At -- ‘ 3.23:: tnent ef release each plane has “has speed cf 135 this. and each at the same height ef 2.fifl km the greund. Altheugh the _'_{:_~ ' are the same. the velecities are iii-Ell at the instant ef release. her plane is flying at an angle ef - - "r i e "iii" _ abeve the hericental and the flying at an angle ef Iii)” bee hericental. Find the magni- 'jg_':;1:m directien ef the velecity with which the fuel tank hits the =__,-u.- ifit is frem [a] plane A and [bi plane E. In each part. give -.3I:E;i'_i' . ‘eual angles with respect tn the herixental. eye” A criminal is escaping acress a reeftep and runs eff the reef : «u : ly at a speed ef 5.3 this. heping te land en the reef ef an ad— .huilding. Air resistance is negligible. The hericental distance at the twe buildings is e. and the reef ef the adjacent building belew thejumping-eff peint. Find tlte maximum value fer D. 1?. backgreund fer this prehlem can be feund in Multiple- Example 2. [in a spacecraft twe engines fire fer a time ef gives the craft an aeceleratien in the x directien ef a. = - .iu while the ether predeces an acceleratien in the y directien 7.3{l en's}. At the end ef the firing peried. the craft has velec- . n nts ef cl. = 3735 nus and c_.. = 43115 ntls. Find the mag- ;and directien cf the initial velecity. Express the directien as an 'th respect te the +.r axis. . ctlve Laarnianara 3.2 at www.wiley.eemfcellegefeutnell : _.'::-.- a review ef the eeneepts in this prehlem. {In a distant planet. 'i; bet as pepular as it is en earth. A gelfer tees eff and drives the lilacs as far as he weuld have en earth. given the same initial ."i'wrr en beth planets. The ball is launched at a speed cf 45 rnfs le cf 29" abeve the herixental. When the hall lands. it is at -:_.;f'u- level as the tee. De the distant planet. what are {a} the r _ I'd ._ t height and {h} the range ef the hall? A fire hese ejects a stream ef water at an angle ef 351')" herisental. The water leaves the nexale with a speed ef . Assuming that the water behaves like a prejectile. hew far I-huilding sheuld the fire hese he leeated te hit the highest pes- .;.l A ball is threwn upward at a speed as. at an angle cf 52“ helicental. It reaches a maximum height ef 7.5 m. Hew _ hi this ball ge if it were threwn straight upward at speed un'i' lamajer-league pitcher can threw a baseball in excess ef Ifa ball is threwn herixentally at this speed. hew much will the time it reaches a catcher whe is llfl m away frem the '_ release? .: rback claims that be can threw the feetball a hericental =;:-- cf Iss rn {see yd}. Furthen‘ndre. he claims that he can de .Z-launcbing the ball at the relatively lew angle ef 3fl.fi" abeve PROBLEMS as the herixental. Te evaluate this claim. determine the speed with which this quarterback must threw the ball. Assume that the ball is launched and caught at the same vertical level and that air resistance can be ignered. Fer cemparisen. a baseball pitcher whe can accu- rately threw a fastball at as mi's [lflfl mph] weuld be censidered exceptienal. II'. 31. earn m Multiple—fleecept Example 4 prevides useful back— greund fer this prehlem. A diver runs hericentally with a speed ef Lit} tru‘s eff a platferm that is fill} at abeve the water. What is his speedjust befere striking the water? 32. The perspective previded by Multiple-Cencept Example 9 is useful here. The highest barrier that a prejectile can clear is 13.5 m. when the prejectile is launched at an angle ef lift“ abeve the heri- taental. 1it‘ll'hat is the prejectile‘s launch speed? 33. Censull Multiple-Cencept Example 4 fer backgreand befere be- ginning this preblem. Suppese the water at the tap ef Niagara Falls has a hericenta] speed cf 2.? mfsjust befere it cascades ever the edge ef the falls. At what vertical distance belew the edge dees the velec- ity vecter ef the water peint dewnward at a 35° angle'belew the herixental? 34. @ In the absence ef air resistance. a prejectile is launched frem and returns te greund level. It fellews a trajectery similar in that in Figure 3.” and has a range cf 23 m. Sappese the launch speed is deubled. and the prejectile is fired at the same angle abeve the greund. What is the new range“? 35. A recket is fired at a speed ef T51] nus frem greund level. at an angle ef film" abeve the heriaental. The recket is fired teward an I i.[l—m-high wall. which is leeated 2H} m away. The recket attains its launch speed in a negligibly shert peried ef time. after which its engines shut dewn and the racket cuasts. By hew much dues the recket clear the tep ef the wall“? as. A rifle is used te sheet twice at a target. using identical car- tridges. The first time. the rifle is aimed parallel in the greund and di— rectly at dte center ef the bull's-eye. The bullet strikes the target at a distance ef H... belew the center. bewever. The secend time. the rifle is similarly aimed. but frem twice the distance frem the target. This time the bullet strikes the target at a distance ef H... belew the center. Find the ratie Haiti-IA. * 31'. earn An airplane with a speed ef 915 mix is climbing upward at an angle ef 5fi.t}“ with respect te the herixental. When the plane’s air titude is T33 m. the pilet releases a package. {a} Calculate the dis“ tance aleng the greund. measurgd frem a peint directly beneath the paint ef release. te where the package hits the earth. (h) Relative tn the greund. determine the angle ef the velecity vecter ef the package just befere impact. * 33. A child eperating a radie-centrelled medal car en a'deek acci— dentally steers it eff the edge. The car‘s displacement 1.] s after leav- ing the deck has a magnitude ef 'i'fl m. What is the cars speed at the instant it drives eff the edge ef the deck? * 35'. As an aid in werking this prehlem. censult Interactive Eelutlen ass at www.wiley.centfeellegeicntnell. A seeeer player kicks the ball teward a geal that is “5.3 min frent efhim. The ball leaves his feet at a speed ef lfxfl ntfs and an angle ef 281i“ abme the greund. Find the speed ef the ball when the gealie catches it in frent ef the net. * 40. See Multiple-Cencept Example 9 fer the basic idea behind preb- lems such as this. A diver springs upward frem a heard that is three meters abeve the water. At the instant she centacts the water her speed is flflfl en's and her bedy makes an angle ef T533" with respect tn the hericental surface ef the water. Determine her initial velecity. beth magnitude and directien. '4... l' -|'|I--I—' —'-'I-. ul'r- .‘Ll'h-“J. EA EHAPTEH a HlHEMATICE lH TWD DIMENSIDHS *4]. Review Ilift'rnceptual Example 5 and |[heartened Simulntlen 3.1 at www.wiley.centfcellegeicutatell hefnre beginning this prnblem. Yen are traveling in a cenvettihle with the tap dnwn. The car is meving at a censtant velecity el 25 ntr's. due east alnng flat grnund. ‘r'eu threw a inmate straight upward at a speed et' 1 i this. Hew far has the car meved when ynu get a chance te catch the tnmate? *41. In the javelin threw at a trackrandntield event. the javelin is launched at a speed at 29 mis at an angle nl' 3st abeve the heriann- tal. As the javelin travels upward. its velecity pnints abeve the heri- aental at an angle that decreases as time passes. Hew much time is required fer the angle tn be reduced frnm 36“ at launch tn i3“? *43. item were his preparatien fer this preblem. review Cnnceptual Esample It}. The twe stenes described there have identical initial speeds at at“ = Ill} nuts and are threwn at an angle a = 3fl.tl”. nne betnw the herianntal and nne abeve the heriznntal. What is the dis- tance benveert the pnints where the stencs strike the grnund‘i *44. Multiple-Cencept Esample 4 deals with a situatinn similar tn that presented here. A marble is tltrewn herianntally with a speed et‘ [5 rats i‘rnm the tep nf a building. When it strikes the grnund. the marble has a velecity that makes an angle cf 65" with the heriaental. Frntrt what height abeve the grnund was the marble threwn'? *45. The leb in tennis is an effective tactic when ynur nppenent is near the net. It censists ef letting the hall ever his head. fnrcing him te meve quickiy away item the net {see the drawing]. Suppese that yes leb the ball with an initial speed ef till this. at an angle ef Still" abeve the hnriaental. At this instant ynur eppnnent is ltlfl m away hem the ball. He begins meving away frnm ynu {13D s later. heping te reach the hall and hit it back at the mnment that it is 2. it} in abeve its launch paint. With what minimum average speed must he meve'i' (Ignere the fact that he can stretch. sn that his racket can reach the hall befere he dees.} “4th Cnncnp’t Bimulntien 3.2 at www.wlley.cnmfcellegefcutneil reviews principles in this prnbiem. a prnjectile is launched frem grnund level at an angle nf llfl" abeve the herianntal. It returns tn grnund level. Tn what value shnuld the launch angle be adjusted. with- nut changing the launch speed. an that the range deuhles‘? ** 41'. item The drawing shews an esaggerated view at a rifle that has been “sighted in" fer a 91.4-meter target. If the muzzle speed ef the bullet is t!” = 42? mis. what are the twe pessible angles ii. and til1 be- tween the rifle barrel and the herianntal such that the bullet will hit the target? One ef these angles is an large that it is nemr used in target sheeting. (Hint: The fritters-ing trigenemetrr'c identity may he asefnt: 2 sin ti ens ti = sin 25'.) ** 43. In the annual battle ef the deems. students gather en the reefs nf lacksen and Walten derms te launch water balleens at each ether with slingshets. The herisnntal distance between the buildings is 35H m. and the heights at the lacksen and Walten buildings are. re- spectively. lid m and 22.0 m. Ignnre air resistance. [a] The first balteen launched by the Jacksnn team hits Walten denn 1i] s after launch. striking it halfway between the grnund and the reef. Find the directinn ef the balieen‘s initial velecity. Give yeur answer as an an- gle measured abeve the herisental. {It} A. secend hallenn launched at the same angle hits the edge Inf Waltenh reef. Find the initial speed ei‘ this secend balleen. H 49. team Frem the tep at" a tall building. a gun is fired. The bullet leaves the gun at a speed nl' 34D refs. parallel tn the grnund. fits the drawing shews. the bullet puts a heie in a windnw nf anether build- ing and hits the wall that faces the windnw. Using the data in the drawing. determine the distances D and H. which tecate the paint where the gun was fired. Assume that the bullet dues net slew dewa as it passes thrnugh the windnw. 34c me. . Bullet in wall H Hele in win-dew n.sn m ** 50. A small can is hanging item the ceiling. A rifle is aimed directly at the can. as the figure il- lustrates. At the instant the gun is fired. the can is released. lgnere air resistance and shew that the bullet will always strike the can. regardless ef the initial speed cf the bullet. Assume that the bullet strikes the can befere the can reaches the grnund. ** 51. a. placekicker is abnut tn kick a field gas]. The ball is 26.9 I'll frem the gnatpest. The bait is kicked with an initial velecity ni ' 19.3 mr‘s at an anglg ti abeve the grnund. Between what twe angles, ti. and it}. will the ball ciear the 2.?4-m-high cressbar‘? (Hint.- Titeva renting trigertemerr't'c identifier may he usefirl: sec ii = lJ'IEc-ns E") and see2 it = l + tan2 3.] Sectien 3.4 Relative Veleeity 52. Twe cars. A and E. are traveling in the same directinn. altheuglt car A is 136 nt behind car E. The speed ei" .4. is 24.4 mils. and the speed ef B is 13.6 mils. Hew much time dees it take fer A in catch B? 53. um r5. swimmer. capahle ef swimming at a speed cf [.4 nits in still water {i.e.. the swimmer can swim with a speed ef 1.4 mr's rela- tive tn the water). starts in s‘tvit'rt directly acrnss a 2.3-km-wide rivet Hewever. the current is ill-ii this. and it carries the swimmer dewn- stream. {a} Hew leng dees it take the swimmer tn cress the riverl [hi Hew far dewnstream will the swimmer be upen reaching the ether side ef the river? 54. @ Twu friends. Barbara and Neil. are net rnllerblading. W' respect tn the grnund. Barbara is skating due snuth at a speed i 4.0 mr's. Neil is in frent ef her. With respect in the grnund. Neil ' -"'.f-_?I_:...; due west at a speed of 3.2 rots. Find Neil’s velocity [magni- lattd'direction relative to due west). as seen by Barbara. the escalator that leads down into a submay station has a length of 325;: s and a speed of is the relative to the pests. a studem is com- : _ oi the station by running in the wrong direction on this escala- -. local record time for this trick is 1 l a. Relative to the escalator. ii" 'tpccd must the student exceed in order to beat the record?JI officer is driving due north at a constant speed of 29 rnt's 'i're to the ground when she notices a truck on an east-west high- of her. driving west at high speed. She finds that the : speed relative to her car is 43 mils {about Ilfl‘ mph). {all . 5. I the vector triangle that shows how the truck's velocity relative _ grated is related to the police car‘s velocity relative to the to the truck‘s velocity relative to the police car. The not be to scale. but the velocity vectors should be ori- stttt hear the appropriate letters. at] What is the _ relative to the ground? ‘I‘wc passenger trains are passing each other on adjacent -' A. is moving east with a speed of i3 this. and train B is west with a speed of 23 mis. ta] What is the velocity -. " + - and direction) of train it. as seen by the passengers in train {ff _}What is the velocity [magnitude and direction} of train E as the passengers in train it? .5251”. -:a picasnre cruise a boat is traveling relative to the water at a ill this due soudt. Relative to the boat. a passenger walks this back of the boat at a speed of 1.5 mt‘s. ta} What is the t- and direction of the passenger’s velocity relative to the . [b] How long does it take for the passenger to walk a dis- - rrt on the boat‘lI {c} How long does it take for the passen- . iii-1:- a distance of 2? m on the water? are in a hot-air balloon that. relative to the ground. has a ve- - till this in a direction due east. You see a hawk moving di- from the balloon in a direction due north. The speed of relative to you is 211 hits. What are the magnitude and di- cf the hawk’s velocity relative to the ground? Express the ' ' angle relative to due cast. .;I -'.'I=I*I at - .- " The captain of a plane wishes to proceed due west. The - speed of the plane is 245 mt's relative to the air. A weather = indicates that a 3311-an wind is blowing from the south to the ' Illlhil Psaattus iii spacecraft, two engines are tumed on for ass s at a moment velocity at the start has .t and y components of a... = am this = sass Eli's. While the engines are firing. the craft undergoes a ELI-m at that has components ch: = 4.11 it it)" or and y = fill? ' in Find the x and y components of the craft’s acceleration. '--volleyball is spiked so that it has an initial velocity of [5 nuts downward at an angle of 55“ below the horizontal. What is ntal component of the hall's velocity when the opposing the hall? spider crawling across a table leaps onto a magazine blocking = The initial velocity of the spider is {with mr's at an angle of the table. and it lands on the magazine illi‘ii'il s after table. Ignore air resistance. How thick is the magazine? ' 'j__--:: year answer in millimeters. -.-- Interactive Learningwttre 3.1 at www.wi1ey.eomt‘collegei '-;"in preparation for this problem. The acceleration due to grav- _:,__f moon has a magnitude of Lb! mlsz. Examples d—B deal ADDITIDHAL PRDBLEME 55 north. ln what direction. measured with respect to due west. should the pilot head the plane? "‘ til. A person looking out the window of a stationary train notices that raindrops are falling vertically down at a speed of it} this rela- tive to the ground. When the trairt moves at a constant velocity. the raindrops make an angle of 25" when they move past the window. as the drawing shows. How fast is the train moving? * as. Q Relative te the ground. a est- has a velocity st tao mt's. ts- rested due north. Relative to this car. a truck has a velocity of 24h mt's. directed 51d“ north of east. What is the magnitude of the truck’s velocity relative to the ground? * 153. Item Mario. a hockey player. is skating due south at a speed of It} this relative to the ice. A teammate passes the puck to him. The pack has a speed of 1 Li] this and is moving in a direction of 22" west of south. relative to the ice. What are the magnitude and direction [relative to due south) of the puclt‘s velocity. as observed by Mario? ** 154. A jetllner can fly dill} hours on a full load of fuel. Wid'tcut any wind it files at a speed of 2.4ll it ll}2 mils. The plane is to make a mend-trip by heading due west for a certain distance. turning around. and then heading due cast for the return trip. During the entire flight. however. the plane encounters a SIS-nits wind from the jet stream. which blows from west to east. What is the maximum distance that the plane can travel due west and just be able to return home“? ** 155. sun can a Coast Guard ship is traveling at a constant velocity of 4.2t1 nits. due east, relative to the water. [in his radar screen the naviga- tor detects an object that is moving at a constant velocity. The object is located at a distance of 2310 m with respect to the ship. in a direction 32d” south of east. Six minutes later. he notes that the object‘s position relative to the ship has changed to 11211} m. Elli” south of west. What are the magnitude and direction of the velocity of the object relative to the water? Express the direction as an angle widt respect to due west. ‘rlifir's I.‘ with a placekicker kicking a football. Assume that the ball is kicked on the moon instead of on the earth. Find [a] the maximum height H and {b} the range that the ball would attain on the moon. Tit. The 1994 Winter Glympics included the aerials competition in skiing. In this event skiers speed down a ramp that slopes sharply ups ward at the end. The sharp upward slope launches them into the air. where they perform acrohatic maneuvers. In the women‘s competi- tion. the end of a typical launch ramp is directed 63" above the hori- zontal. With this launch angle. a skier attains a height of 13 rn above the end of the ramp. What is the skier’s launch speed? T1. lent Fin eagle is flying horizontally at 6.0 mils with a fish in its claws. It accidentally drops the fish. [a] How much time passes be- fore the fish’s speed doubles? [it] How much additional time would be required for the fish’s speed to double again“? T1. Baseball player A hunts the ball by hitting it in such a way that it acquires an initial velocity of 1.9 [[le parallel to die ground. Upon contact with the hat the hall is 1.2 m above the ground. Player E —I..I.l -- -.n..__..-_-.n.-_. .1._. EB enaeren e KINEMATICS IN Tch DIMENSIDNE wishes tn duplicate tltis hunt, in an far as he else wants tn give the hall a vet-deity.r parallel tn the grnund and have his hall travel the same hnr- ianntal distance as player A‘s hall duesr Hnwever. player B hits the ball when it is [.5 at ahnve the grnund. What is the magnitude nf the initial veins:in that player B's hall must be given? * 73. Eefnre starting this prnhlem cnnsult Interactive Eeluflen 3.13 at www.wilepenmrcnllegelcutnell. A gnlfer. standing nn a fairway. hits a shnt tn a green that is elevated 5.5fl ttt ahnve the pnint where she is standing. If the hall leaves her club with a velneity nf 461} mils at an angle nf Sill" ahnve the greund. find the time that the hall is in the air hefnre it hits the greenr * T4. In a stunt heing hinted fer a mnvie. a spurts ear nvet'takes a truck tnwing a ramp. drives up and nff the ramp. sears late the airr and then lands nn tnp nl' a flat trailer heing tnwed by a secnnd truck. The tnps nf the ramp and the flat trailer are the same height ahnve the read. and the ramp is inclined in” above the hnrisnntal. Elnth trucks are driving at a ennstant speed nf ll mils. and the flat trailer is IS nt frnrn the end ni' the ramp. Neglect air resistance, and assume that the ramp changes the direetinn. hut net the magnitude. nf the car’s initial veincity. What is the minimum speed the car must have, relative in the rend, as it starts up the ramp? “‘15. sent An airplane is flying with a velnrcit}r at 240 Inls at an angle uf Hill“ with the hnrianntalr as the drawing shnws. When the altitude ef the plane is 2.4 km, a flare is released frnm the plane. The flare hits the target en the grnund. What is the angle tl’.’ 319” c, * TIE. As an aid in werlting this prehlem, cnnsult Interactive Snlutlen EJE at www.wiley.cnntlcnliegetcutnell. A fen'yhnat is traveling in a directinn 33h” nnrth ni' east with a speed at 5.52] this relative tn the water. A passenger is walking with a velncity nf 2.511} rnls due east rel- ative tn the hnat. What is the velncity (magnitude and directinn} nf the passenger with respect tn the water“?I Determine the directinnal angle relative tn due east. ’1' "IT. First review Interactive Selutlen 3.1? at IIIrvrvr.Irri]ep.enntlenllegr.-lI ctttttell. After leaving the end {If a slti ramp. a ski jumper lands EltJWl‘t- hill at a pnth that is displaced SI 1} m hnriznntallj.I item the end all the ramp. His vein-city, just hefnre landing, is 23D mils and pnittts in a di- rectinn 43D” helnw the hnrianntal. Neglecting air resistance and any lift he esperiences while airhnrne, find his initial velneitj,r [magnitude and directinn} when he left the end hi the ramp. Express the directinn as an angle relative tn the hntianntal. ** 18. Tth heats are heading away.r frnrn shnre. Beat 1 heads due nnrtlt at a speed {If sen rnr's relative in the shnre. Relative tn best i, heat 2 is ntnving sans nnrth nf east at a speed nf Len this. A passenger nII heat 2 walks due east acrnss the deck at a speed nf [fill this relative tn heat 2. What is the speed nf the passenger relative tn the shnre'l ** T9. Twn cannens are rnnunted as shnwn in the drawing and rigged ta fire simultanenusly. They are used in a circtis act in which twn clnwns serve as human cannunhalls. The clnwns are fired tnward each ether and cnllide at a height nf Lilli} in ahnve the measles nt‘ the eannnns. Clnwn A. is launched at a Till” angle. with a speed nl' 911i] mi‘s. The hnrianntal separatinn between the clnwns as the}.r leave the cannnns is hill} m. Find the launch speed em and the launch angle dB [L‘s-45.93} fnr clnwn B. Ufl‘g = gflfl IT'IJrS Um; ...
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This note was uploaded on 11/01/2009 for the course PHYS 122 taught by Professor Thorns during the Winter '09 term at The School of the Art Institute of Chicago.

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3-2 - as tel-interest a HtHEMATICE tH TWD DIMENSIONS the...

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