t s (half of the total time in the air) d?


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1 .. In Cl or Homework Eercie. An Olmpic long jumper i cpble of jumping 8.0 m. Auming hi horizonl peed i 9.0 m/ he lee he ground, how long w he in he ir nd how high did he go? horizonl? 8.0m 9.0 m / To find ou how high he jumper wen, we mu look eiher he rip up or he rip down. We will ue he rip down o h he iniil ericl eloci will be zero. ericl (uing down poiie) i m / (hlf of he ol ime in he ir)? i 0 (9.80)(0.445) 0.97m. An hlee hrow he hopu wih n iniil peed of 4 m/ 40. o ngle o he horizonl. The ho lee he hopuer hnd heigh of. m boe he ground. Clcule he horizonl diplcemen relled. UNIT D Moion RRHS PHYSICS Pge of 36
2 co (4)(co 40. ) m/ in (4)(in 40. ) 9.0 m/ horizonl ericl (uing up poiie) m /? i 9.0 m / 9.80 m /.m i. 9.0 ( 9.80) m 3. A projecile i fired wih n iniil peed of 63.4 m/ n ngle of 4.6 o boe he horizonl on long fl firing rnge. Deermine. The mimum heigh reched b he projecile UNIT D Moion RRHS PHYSICS Pge of 36
3 co (63.4)(co 4.6 ) 57.6 m/ in (63.4)(in 4.6 ) 6.4 m/ ericl (uing up poiie) i f 6.4 m / 9.80 m / 0? f i ( 9.80) 35.6m b. The ol ime in he ir. f i Since hi i ju he ime o go up, he ol ime in he ir i 5.38 c. The ol horizonl dince coered. horizonl 57.5 m / 5.38? m UNIT D Moion RRHS PHYSICS Pge 3 of 36
4 d. The eloci of he projecile.50 fer firing. The horizonl eloci of he projecile doe no chnge. I will ill be 57.5 m /. We mu find he new ericl eloci. ericl (uing up poiie) i 6.4 m / 9.80 m /.50 f? f i f m / f f f f f f f (57.5) (.7) 58.7 m/ n f f f 58.7 m /,.5 boe he horizonl Noice h he projecile h lowed down nd i more horizonl, one would epec before i reche i highe poin. 4. Triling b wo poin, nd wih onl.00 remining in bkebll gme, P mke jumpho n ngle of 60.0 o wih he horizonl, giing he bll eloci of 0.0 m/. The bll i releed he heigh of he bke, 3.05 m boe he floor. YES! I' core.. How much ime i lef in he gme when he bke i mde? UNIT D Moion RRHS PHYSICS Pge 4 of 36
5 co (0.0)(co 60.0 ) 5.00 m/ in (0.0)(in 60.0 ) 8.66 m/ ericl (uing up poiie) i? 8.66 m / 9.80 m / 0 (ince he bll i releed he me heigh he bke) i ( 9.80) remining b. The hreepoin line i dince of 6.0 m from he bke. Did he P ie he gme or pu hi em hed? horizonl 5.00 m /.77? m Since 6.0m, he bke i worh 3 poin nd he pu hi em hed. UNIT D Moion RRHS PHYSICS Pge 5 of 36
6 5. A cricke bll i hi 30.0 m/ n ngle of 53.0 o wih he horizonl. Immediel, fielder run 4.00 m/ owrd he ber nd cche he bll he me heigh i w hi. Wh w he originl dince beween he ber nd he fielder? Bll co (30.0)(co 53.0 ) 8. m/ in (30.0)(in 53.0 ) 4.0 m/ horizonl ericl (uing up poiie) 8. m /? i ( 9.80) i m / 9.80 m / b b b Fielder 88.7m f f f 9.6m d 08.3m UNIT D Moion RRHS PHYSICS Pge 6 of 36
7 6. A foobll i kicked n ngle of 37 o wih he horizonl wih eloci of 0.0 m/. A fence i 3.0 m w nd i 3.5 m high. Doe he bll go oer he fence? co (0.0)(co 37 ) in (0.0)(in 37 ) 6 m/ m/ We will ume h he bll reche he fence, nd emp o clcule i heigh. horizonl 6 m / ericl (uing up poiie) i m / 9.80 m /? i (.9) ( 9.80)(.9) 5.m The bll i boe he fence, which i onl 3.5 m high. 7. A peron i in moing eleor. He hrow roen egg horizonll ou of he moing eleor wih eloci of 5.0 m/. A he ime of he hrow, he eleor w 8.7 m boe he ground. The roen egg lnded 4. m w from he eleor. Wh w he eloci of he eleor? W he eleor moing up or down? horizonl ericl (uing up poiie) 5.0 m / 4.m 9.80 m / i 8.7m? UNIT D Moion RRHS PHYSICS Pge 7 of 36
8 i 8.7 (0.84) ( 9.80)(0.84) i i 6. m / The eleor w moing downwrd 6. m/. 8. An irplne i in leel fligh eloci of 500. km/h nd n liude of 500 m when wheel fll off.. Wh horizonl dince will he wheel rel before i rike he ground? horizonl ericl (uing down poiie) 500. km / h 39 m /? i (9.80) 7.5 i 0 500m 9.80 m / m b. Wh will he wheel' eloci be when i rike he ground? f i f (9.80) f 7 m / UNIT D Moion RRHS PHYSICS Pge 8 of 36
9 f f f f (39) (7) 0 m/ n 0 m /, 5 from he ground f f Police gen fling conn 85 km/h horizonll in lowfling irplne wih o drop n eploie ono mer criminl' cr relling 45 km/h (in he me direcion) on leel highw 88.0 m below. A wh ngle (wih he horizonl) hould he cr be in heir igh when he bomb i releed? horizonl ericl (uing down poiie) 85 km / h 5.4 m / pg 45 km / h 40.3 m / cg? 9.80 m / i m i (9.80) 4.4 Looking he horizonl, we need o know he eloci of he plne wih repec o he cr o h we cn find ou how much frher he bomb mu rel hn he cr: pg pc cg pc pg cg m/ UNIT D Moion RRHS PHYSICS Pge 9 of 36
10 m So he plne hould be 47. m behind he cr when he bomb i releed. n d The bomb hould be in heir igh n ngle of below he horizonl. 0. A bkebll pler rie o mke hlfcour jumpho, releing he bll he heigh of he bke. Auming he bll i lunched 5.0 o, 4.0 m from he bke, wh peed mu he pler gie he bll? co (co5.0 ) 0.69 in (in 5.0 ) horizonl ericl (uing up poiie) m i m / 0 UNIT D Moion RRHS PHYSICS Pge 30 of 36
11 Subiuing hi ino he equion for ericl moion, i ( 9.80) m /. A eflon hocke puck lide wihou fricion cro ble conn eloci. When i reche he end of he ble, i flie of nd lnd on he ground. For ech of he following queion, drw ll ecor o cle.. Drw he iuion boe, drwing ecor howing he force on he puck wo poiion while i i on he ble nd wo more while i i in he ir. The force of gri ecor hould ll be he me lengh. b. Drw ecor howing he horizonl nd ericl componen of he puck' eloci he four poin. UNIT D Moion RRHS PHYSICS Pge 3 of 36
12 The horizonl eloci componen hould ll be he me lengh; he ericl eloci componen hould be lrger in he fourh digrm hn in he hird. c. Drw he ol eloci ecor he four poin. The ol eloci ecor hould be lrger nd more ericl in he fourh digrm hn in he hird.. Suppoe n objec i hrown n ngle wih he horizonl wih he me iniil eloci on he moon, where g i oneih lrge on Erh. Will he following quniie chnge? If o, will he become lrger or mller?. i nd i Since hee re he iniil eloci componen, he will no chnge (i i hrown wih he me iniil eloci) b. ime of fligh Since he ccelerion i mller, i will ke longer for he ericl eloci o chnge. The objec will herefore be in he ir for more ime. c. mimum heigh Since f i i, mller ccelerion will reul in lrger mimum heigh. UNIT D Moion RRHS PHYSICS Pge 3 of 36
13 d. Rnge Rnge i he horizonl dince relled. Since he objec i in he ir for more ime nd he horizonl eloci i unchnged, he objec will rel furher. 3. A niper on building i ring o hi rge on he ground. The building i 3.0 m high. The niper poin hi rifle poin 49.5 m w from he building. If he bulle rel 35 m/, how fr from he building will he bulle lnd? We mu fir ue he direcion he i iming he gun o clcule he ngle n Thi ngle cn now be ued o clcule he eloci componen. co 35(co 75.3 ) 34.3 m/ in 35(in 75.3 ) 3 m/ horizonl ericl (uing down poiie) 3 m /? i 34.5 m / 9.80 m / 3.0m UNIT D Moion RRHS PHYSICS Pge 33 of 36
14 i (9.80) Since he ime mu be poiie, m 4. Show h he rnge R of projecile, which i defined he horizonl dince relled when he finl poin i he me leel he iniil poin, i gien b he equion in R g where i he iniil eloci of he projecile nd i he ngle wih he horizonl. (Hin: ue he rigonomeric ideni in in co ) co in Since rnge R i he me he horizonl diplcemen, R co R co And ince he ericl diplcemen i zero UNIT D Moion RRHS PHYSICS Pge 34 of 36
15 g i 0 ( in ) ( g) in in g Equing hee gie R in co g R inco g in g 5. Uing he equion gien in queion 4 nwer he following queion.. Auming h he iniil eloci i, wh ngle will proide he mimum rnge? The mimum rnge will be when in h i mimum lue, which i one: in b. Wh minimum iniil eloci mu projecile he o rech rge 90.0 m w? Since we wn he mlle eloci h will he rnge of 90.0, hi mu be he mimum rnge for hi eloci: R R g in g 9.7 m / c. A grden hoe held ner he ground hoo wer peed of 4. m/. A wh ngle() hould he nozzle poin in order h he wer lnd.8 m w? Wh re here wo differen ngle? UNIT D Moion RRHS PHYSICS Pge 35 of 36
16 R in g (6.5) in in or53 4 or 76 There re wo differen ngle becue he rnge of projecile i mmericl round he ngle of 45 o (for emple, 0 o nd 70 o or 40 o nd 50 o ), which proide he mimum rnge. Tr hi wih oher ngle h dd o gie 90 o. 6. A bll i hrown horizonll from he op of cliff wih iniil peed o. A n momen, i direcion of moion mke n ngle of wih he horizonl. Derie formul for funcion of ime. n f o Since he onl unknown rible here i f inoling ime., we need n epreion for hi ericl (uing down poiie) i f 0 g? f f 0 g g f i Subiuing h ino our preiou equion gie g n o g n o UNIT D Moion RRHS PHYSICS Pge 36 of 36
17 7. Two cricke bll re hrown horizonll from he me heigh bu differen peed. The fer bll hi he wicke locion higher hn he lower one doe. Wh doe he fer bll no fll fr he lower one? Afer ll, he rel he me dince nd ccelere down he me re. The lower bll i in he ir for more ime, ince i ke longer o ge o he wicke. Thi gie he bll more ime o fll, o i fll greer dince while in he ir. 8. A huner i ring o hoo monke hnging from ree. A oon he huner fire, he monke i going o le go of he ree. Aume h he huner i below he monke o h he mu ngle he gun upwrd n ngle o im he monke. Should he huner im direcl, boe, or below he monke in order o hi him? Ju in he imilr queion he preiou ecion, he huner hould im direcl he monke. Thi cn be hown below; hi i n dnced problem nd ll rinee hould no be epeced o be ble o proide hi oluion. Monke (uing up poiie) i 0 g m? m i 0 g g So he monke heigh n ime i h h g o where ho i he monke originl heigh. Bulle ho n UNIT D Moion RRHS PHYSICS Pge 37 of 36
18 horizonl ericl (uing up poiie) co i in g b? co co b i in in co n g g g ho Bu n h o d b g h o g I cn be een h he monke heigh i he me he bulle ericl diplcemen ime fer relling horizonl dince ; ince he re he me heigh, he bulle will hi he monke. UNIT D Moion RRHS PHYSICS Pge 38 of 36
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