2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information.


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1 Nme D Moion WS The equions of moion h rele o projeciles were discussed in he Projecile Moion Anlsis Acii. ou found h projecile moes wih consn eloci in he horizonl direcion nd consn ccelerion in he ericl direcion ( = 9.8 m/s ). ou cn use he sme equions from he preious uni o sole projecile moion problems keeping in mind horizonl moion is independen of ericl moion. Use sepre shees o sole problems. Show ll work including digrm of he problem, lis of  nd  ribles h indice iniil nd finl condiions, nd he equions ou use o sole he problem. Horizonll Lunched Projeciles A horizonll lunched projecile s iniil ericl eloci is zero. Sole he following problems wih his informion.. Gien he following siuion of mrble in moion on ril wih negligible fricion. Once he bll lees he ble, clcule how long i will ke for he bll o hi he floor. V = m/s V =m/s h =.5 m De m f.5m 9.8m b. Deermine he impc eloci (mgniude nd direcion) of he mrble righ before i his he floor We need o deermine boh he  nd  componens of he impc eloci nd hen pu hem ogeher o find he D impc eloci ecor. does no chnge so we lred know h ( = m/s) 9.8(.553) 5.4m.4m nq s V = m/s o q 8.5 =.4 m/s, 8.5 o below he horizonl q V =5.4 m/s
2 c. How fr will he bll rel horizonll before hiing he floor? If he ble were 3. m high (so we he doubled he heigh), nd sphere ws reling wih he sme eloci of m/s while on he ble, deermine ech of he following... d. Deermine how much longer i kes he mrble o fll o he floor. Relionship beween Fligh Time nd heigh (consns nd ): see boed equion in ) If he heigh of he ble is doubled, fligh ime increses b e. Wh effec did doubling he heigh he on rnge of he mrble? Wh oher fcors ffec he rnge of he sphere? Rnge depends on (which is unchnged) nd fligh ime So, if he heigh of he ble is doubled, rnge increses b rnge of 3m high ble is oher fcors h ffec he rnge: iniil eloci (if doubled, hen rnge doubled) ccelerion due o gri (if doubled, rnge reduced b /. 7). A bole is dropped from moing irplne (ignore he effec of ir resisnce). If he plne from which he bole ws dropped ws fling heigh of 5m, nd he bole lnds 4m horizonll from he iniil dropping poin, 5 m (.553) 5.53m V g (5.53) 7.8m 4 m ) how fs ws he plne fling when he bole ws relesed? s 4 4m (.) 39.6m 5m 9.8m
3 b) wh ws he eloci of he bole righ before i hi he ground? 9.8(.) 98.98m V =39.6 q V = m nq q o 68. = 6.6 m/s, 68. o below he horizonl (68. o from is) 3. Suppose h n irplne fling 6 m/s, heigh of 3m, dropped sck of flour (ignore he effec of ir resisnce). 6 3m 9.8m ) How fr from he poin of relese would he sck he reled when i sruck he ground? s 6(7.8) 469m b) Wh would be he impc eloci of he sck of flour? 9.8(7.8) 76.64m 76.6 nq 97.3m 6 o q 5 = 97.3 m/s, 5 o below he horizonl q V =6 V =76.6
4 4. In mn locions, old bndoned sone qurries he become filled wih wer once ecing hs been compleed. While snding on qurr wll, bo osses piece of grnie ino he wer below. If he hrows he bll horizonll wih eloci of 3. m/s, nd i srikes he wer 4.5 m w, how high boe he wer is he wll? (ignore he effec of ir resisnce) V =3m/s Projeciles Lunched n Angle Projecile moion nd ecors s 4.5 m.m 3m 4. 5m 4.9(.5 ) 9.8m V V V cosq sinq θ θ V A projecile s eloci () hs n componen ( ) nd componen ( ). The componen ( ) is found b mulipling he mgniude of he eloci b he cosine of he ngle, θ. Similri, he componen of eloci is found b mulipling he mgniude of he eloci b he sine of he ngle, θ. So, projecile fired m/s 65 o hs n eloci of cos 65 or 8.5 m/s. The projecile would he eloci of sin 65 or 8 m/s. So, he projecile would fire s fr s one fired horizonll 8.5 m/s nd s high s one fired srigh up 8 m/s. 5. A lcrosse pler slings he bll n ngle of 3 degrees boe he horizonl wih speed of m/s.
5 cosq cos 3 7.3m ) How fr w should emme be in order o cch he bll he sme heigh i ws relesed? 4.9.4s b) Wh is he eloci of he bll righ before i is cugh? Since he bll lnds he sme heigh s i ws lunched, ime up is equl o ime down. Therefore, finl speed is equl o iniil speed; direcion of finl eloci below he horizonl he sme moun s he iniil ws boe. = m/s, 3 below he horizonl (3 from is) c) Wh is he bll s mimum heigh? Concepull, bll rels up for s erge ericl eloci of 5m/s ( =/ ( )), so i goes o m heigh of = = 5m/s cos 3 7.3m/ s m m 9.6 c) Wh is he bll s eloci he pek? = pek, =7.3 m/s. Therefore, pek = 7.3m/s, in direcion sinq sin 3 m 9.8m 7.3(.4) 35.3m sin 3 m m 5.m 9.8m
6 6. A dredeil is sho ou of cnnon n ngle of 45 o wih n iniil speed of 5 m/s. A ne is posiioned horizonl disnce of 5 m from he cnnon. A wh heigh boe he cnnon should he ne be plced in order o cch he dredeil? V 45 V 5m cosq 5cos m 5m 5sin m sinq 9.8m s.9m 7.7(.8) 4.9(.8 ) 7. Frusred wih he book ou re reding, ou open he second sor clssroom window nd iolenl hurl our book ou he window wih eloci of 8 m/s n ngle of 35 degrees boe he horizonl. If he lunch poin is 6 meers boe he ground, 6 m 35 o V V cosq 8cos sin m sinq 9.8m
7 ) how fr from he building will he book hi he prking lo? s or.48s b) Wh will he impc eloci of he book be? 37.9m f 5 nq 4.7 m o q 45.6 f = m/s, 45.6 below he horizonl (45.6 from is) 4.7(.58).3 9.8(.58) 5.m q V =4.7 V =5. 8. A bll is hrown srigh upwrd nd reurns o he hrower's hnd fer 3 seconds in he ir. A second bll is hrown n ngle of 3 degrees wih he horizonl. A wh speed (remember h his is he resuln mgniude of he ericl nd horizonl speeds) mus he second bll be hrown so h i reches he sme heigh s he one hrown ericll? V 3 V V Since he ericl moion of he projecile is independen of he horizonl componen, he projecile s ericl componen mus be idenicl o he free fll. To rech he sme heigh s he bll hrown srigh up, he projecile nd he srigh up bll mus he he sme iniil ericl elociies. OR he mus be in ir for he sme ime (3 sec). Since he mus boh rech pek in.5s (nd loose ll ericl eloci in.5s), he iniil ericl eloci mus be 5m/s ou could lso find he iniil ericl eloci using kinemic equions: Bll up m 3s 5m (3) 5(9)
8 Projecile Bll Wih he ngle nd, cn use rig o find : sin 3 sin m
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