ANSWERS Prjecle mn s he ecrl sum w ndependen elces, hrznl cmpnen nd ercl cmpnen. The hrznl cmpnen elcy s cnsn hrughu he mn whle he ercl cmpnen elcy s dencl ree ll. The cul r nsnneus elcy ny pn lng he prblc ph s ngen he prbl nd equl he ecrl sum he hrznl nd ercl cmpnen elces. The ercl cmpnen he elcy ny pn gng up equls he ercl cmpnen he elcy he equlen pn cmng dwn (bu ppse n drecn). = Rnge egh NOTE: In slng prblems n prjecle mn, wrk u he ercl nd hrznl cmpnen elces seprely s hey were w sepre prblems. Use 0 m/s r he ccelern due gry.. Tw snes, A nd B, re used n n expermen. A he sme me h sne A s drpped, sne B s hrwn hrznlly wh elcy 5 m/s. Fr ech secnd ll, ll n he elces bh snes, s ndced. (Yu need n nclude he uns) A = 0 = s = s = 3 s Sne = = = = 0 0 0 30 Sne B = 0 = 0 = 5 = s = 0 = 5 = s = = 0 5 = 3 s = = 30 5 = 4 s = 40 = 4 s = = 40 5 = 5 s = 50 = 5 s = = 50 5 PYSICS 534 DYNAMICS Physcs Ex-3.DOC 999 S. Lncne Pge /6
. A sne s drpped rm blcny 0 m hgh. w lng des ke he sne rech he grund? [ s] s 0 m / s s (0 m / s )(0 m) 400 m / s s 0 m / s 0 m / s 0 m/s 3. A bll s hrwn hrznlly rm 0 m hgh cl wh elcy 0 m/s. w r rm he bse he cl des he bll lnd? [0 m] s h = 0 m 0 m / s 0 m / s s s s 0 m / s 0 (0 m / s )(0 m) 0 ( )( s) 0 m 0 m / s 4. A bll s hrwn n he r wh elcy 0 m/s n ngle 60 rm he hrznl. Clcule: ) w hgh rses (he hegh). [5 m] Rnge =? ercl (0 m / s)sn60 (0 m / s)(0.866) 7.3 m / s 0 7.3 m / s.73 s 0 m / s 0 7.3 m / s s ( ) ( )(.73 s) 4.96 m 5 m b) w r rels (he rnge). [35 m] hrznl (0m / s)(cs60 ) (0m / s)(0.5) 0 m / s Rnge ( ) (0m / s)(.73s)() 34.6 m 35 m hrznl 0 m/s 60 egh =? PYSICS 534 DYNAMICS Physcs Ex-3.DOC Prjecle Mn Pge /6
5. A bll s hrwn n he r wh elcy 0 m/s n ngle 45 rm he hrznl. Clcule: ) w hgh rses (he hegh). [0 m] 0 m/s 45 egh =? Rnge =? 4 m / s 0 0 m / s 0 4 m / s 4 m / s 0 4 m / s 4 m / s r 0 m / s.4 s s (7 m / s)(.4 s) 9.8 m 0 m 7 m / s b) w r rels (he rnge). [40 m] s (4 m/s)(.4 s) 39.5 m 40 m 6. A bll s hrwn n he r wh elcy 0 m/s n ngle 30 rm he hrznl. Clcule: ) w hgh rses (he hegh). [5 m] (0 m / s)(sn 30 ) 0 m / s s ( 0 0 m / s s 0 m / s 0 0 m / s ) ( )( s) 5 m b) w r rels (he rnge). [35 m] 0 m/s 30 egh =? Rnge =? Snce he me gng up s s, he l me (up nd dwn) s s. (0 m / s)(sn 60 ) 7.3 m / s Rnge (7.3 m / s)( s) 34.6 m 35 m PYSICS 534 DYNAMICS Physcs Ex-3.DOC Prjecle Mn Pge 3 /6
7. Fll n he ble belw wh yur nswers rm quesns 4, 5 nd 6 be. Quesn Inl elcy Angle egh Rnge ) 4 0 m/s 60 5 m 35 m b) 5 0 m/s 45 0 m 40 m c) 6 0 m/s 30 5 m 35 m d) Whch ngle prduces he grees hegh? 60 e) Whch ngle prduces he grees rnge? 45 8. A cnnn bll s red n he r n ngle 40 rm he hrznl nd rses 5 m. Clcule s rnge. [3.8 m/s] Fnd he me kes n bjec ll s r 5 m 0 (0 m /s ) r s r Fnd he ercl cmpnen he nl elcy. s s r 0 ( 0 m /s )(5 m) r 0 m /s Fnd he hrznl cmpnen he nl elcy. Tn 40 0 m /s r 0 m /s Tn 40 Fnd he rnge. Tme = s g up + s cme dwn. Rnge (.9 m /s)( s) 3.8 m reely 5 m..9 m /s s 9. A bll s hrwn n he r rm cl 0 m hgh. I he Sep bll : s hrwn wh elcy 5 m/s n ngle 30 Clculn ercl nd hrznl cmpnens elcy. be he hrznl, clcule hw r (5 m / s)(sn 30 ) 7.5 m / s rm he bse he cl he bll hs he grund. (5 m / s)(cs 30 ) 3 m / s [37.7 m] Sep : Clculn me rech hghes pn. 0 7.5 m / s r 0.75 s 0 m / s Sep 3 : Clculn hegh be cl. 0 7.5 m / s s ( ) ( )(0.75 s).8 m Sep 4 : Clculn me ll rm heghes pn grund (0 m.8 m). s (.8 m) s 0 r 4.56 s Thus :.4 s 0 m / s Sep 5 : Clculn rnge. Rnge (3m / s)(0.75 s.4 s) 37.57 m 38 m 5 m/s 30 h = 0 m PYSICS 534 DYNAMICS Physcs Ex-3.DOC Prjecle Mn Pge 4 /6
0. A bll s hrwn n he r rm cl 0 m hgh. Tkephemhsmplespsble, I unshebenleunhermuls. he bll s hrwn wh elcy 5 m/s n ngle 30 belw he hrznl, clcule hw r rm he bse he cl he bll hs he grund. Sep : Clculn ercl nd hrznl cmpnens elcy. [8. m] (5)(Sn 30 ) 7.5 m / s (5)(Cs 30 ) 3 m / s Use qudrc equn : 7.5 0 0 Sep : Clculn me ll (0 m). A 5 B 7.5 C 0 B B 4AC s A r 0 7.5 5 7.5 (7.5) 4(5)( 0) (5) r 5 7.5 0 0 7.5.4 7.5.4.4 s.39.4 s 0 0 (Dsregrd nege lue) Sep 3 : Clculn rnge. Rnge (3)(.4) 8. m 5 h = 0 m 30 5 m/s. A prjecle s red n he r wh such nl elcy h s hegh s m nd Clculn s rnge ll s me 48 ( m. meers) : s Deermne he nl elcy he prjecle. [.9 (0 m/s, m / m 0 s 45 ) N E] 4 m.4 s 0 m / s.55 s Clculn ercl cmpnen nl elcy (rm ree ll) : s s (0 m / s )(m) 0 40 m / s 5.5 s Clculn hrznlcmpnen nl elcy (rm rnge) : Rnge Rnge 48 m (.55 s) s 5.5 m / Clculn nl elcy : Mgnude :.9 m / s Drecn: Tn A 48 m 3. s 5.5 m / s 5.5 m / s Answer :.9 m / s 45 N E (5.5 m / s) (5.5 m / s) 480.5 m / s A 45 =? A =? egh = m Rnge = 48 m PYSICS 534 DYNAMICS Physcs Ex-3.DOC Prjecle Mn Pge 5 /6
. A helcper s rsng erclly 5 m/s. When s hegh 00 m be he grund, res prjecle hrznlly wh elcy 50 m/s. Deermne: ) The me kes he prjecle h he grund. [8 s] Ne: A he ns n he prjecle s red, sn ce he helcper s gng up, hs nege elcy. Thus, s 00 m h = 00 m B 5 m/s Usn g he qudrc equn : 3 40 0 A B 3 C 40 50 m/s _ 5 m /s A ( 3) 3 9 60 _ 3 3 3 3 6 r 8 s (Dsregrd nege lue) _ r s 00 5 5 5 0 m /s 5 00 0 3 40 0 B 4AC ( 3) 4()( 40) () b) The hrznl dsplcemen. [400 m] _ Ne h he helcpers relng 50 m / s hrznlly. Thus : _ s (50 m / s)(8 s) 400 m PYSICS 534 DYNAMICS Physcs Ex-3.DOC Prjecle Mn Pge 6 /6