RELAIVE MOION Conens opic Page No. heory 01 Exercise - 1 0-07 Exercise - 08-09 Exercise - 3 09-11 Exercise - 4 1 Answer Key 13 Syllabus Relaive Velociy Name : Conac No. ARRIDE LEARNING ONLINE E-LEARNING ACADEMY A-479 indra Vihar, Koa Rajashan 34005 Conac No. 8033545007
RELAIVE MOION RELAIVE VELOCIY : Velociy of A relaive o B is given by r V r r AB = VA -V. B V r AB refers o he velociy which A appears o have as seen by B. he above idea of 1 dimensional relaive moion can be exended o moion in dimensions. (a) For crossing a river in minimum possible ime, he velociy of he swimmer relaive o he river should be perpendicular o he river flow. (b) If an ahelee is running, his clohes will be furling in he direcion of he velociy of he wind relaive o him self. (c) If you do no wan o ge drenched in a rain, you should hold he umbrella in a direcion opposie o he velociy of he rain relaive o your self. (d) wo paricles, 1 and, move wih consan velociies v 1 and v. A he iniial momen heir radius vecors are equal o r 1 and r. For he wo paricles o collide, he relaive velociy of 1 wih respec o should be direced owards 1 as seen by. A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 1
PAR - I : OBJECIVE QUESIONS * Marked Quesions are having more han one correc opion. Secion : (A) Relaive moion A-1. A rain is sanding on a plaform, a man inside a comparmen of a rain drops a sone. A he same insan rain sars o move wih consan acceleraion. he pah of he paricle as seen by he person who drops he sone is : (A) parabola (B) sraigh line for someime & parabola for he remaining ime (C) sraigh line (D) variable pah ha canno be defined. A-. wo rains A & B 100 km apar are ravelling owards each oher on differen racks wih saring speed of 50 km/h for boh. he rain A acceleraes a 0 km/h and he rain B reards a he rae 0 km/h. he disance covered by he rain A when hey cross each oher is : (A) 45 km (B) 55 km (C) 65 km (D) 60 km A-3. A-4. A-5. A-6. wo paricles are moving wih velociies v 1 and v. heir relaive velociy is he maximum, when he angle beween heir velociies is : (A) zero (B) p/4 (C) p/ (D) p A car A is going norh eas a 80 kmh 1 and anoher car B is going souh eas wih a velociy of 60 kmh 1. he velociy of A relaive o B makes an angle wih he norh equal o (A) - æ ö an ç è7 ø 1 (B) - æ ö an ç è ø 1 7 (C) -1 an (7) (D) - æ ö an ç. 7 è ø. A coin is released inside a lif a a heigh of m from he floor of he lif. he heigh of he lif is 10 m. he lif is moving wih an acceleraion of 11 m/s downwards. he ime afer which he coin will srike wih he lif is : (A) 4 s (B) s (C) 4 1 s (D) s 11 A ship is ravelling due eas a 10 km/h. A ship heading 30 eas of norh is always due norh from he firs ship. he speed of he second ship in km/h is - 1 1 (A) 0 (B) 0 3 / (C) 0 (D) 0/ A-7. A-8. hree ships A, B & C are in moion. he moion of A as seen by B is wih speed v owards norh eas. he moion of B as seen by C is wih speed v owards he norh wes. hen as seen by A, C will be moving owards (A) norh (B) souh (C) eas (D) wes A man in a balloon, hrows a sone downwards wih a speed of 5 m/s wih respec o balloon. he balloon is moving upwards wih a consan acceleraion of 5 m/s. hen velociy of he sone relaive o he man afer second is : (A) 10 m/s (B) 30 m/s (C) 15 m/s (D) 35 m/s A-479 Indra Vihar, Koa Rajashan 34005 Page No. #
A-9. A-10. hree sones A, B and C are simulaneously projeced from same poin wih same speed. A is hrown upwards, B is hrown horizonally and C is hrown downwards from a building. When he disance beween sone A and C becomes 10 m, hen disance beween A and B will be : (A) 10 m (B) 5 m (C) 5 m (D) 10 m A body is hrown up in a lif wih a velociy u relaive o he lif and he ime of fligh is found o be '. he acceleraion wih which he lif is moving up is : (A) u - g (B) u - g (C) u + g (D) u + g A-11. Shown in he figure are he velociy ime graphs of he wo paricles P 1 and P. Which of he following saemens abou heir relaive moion is rue? Magniude of heir relaive velociy : (consider 1-D moion) (A) is zero (C) coninuously decreases (B) is non-zero bu consan (D) coninuously increases Secion : (B) Relaive moion in river flow & Air flow B-1. he speed of boa is 5 km/h in sill waer. I crosses a river of widh 1 km along shores possible pah in 15 min. he velociy of river waer is (A)1 km/h (B) 3 km/h (C) 4 km/h (D) 5 km/h B-. A man is crossing a river flowing wih velociy of 5 m/s. He reaches a poin direcly across a a disance of 60 m in 5 sec. His velociy in sill waer should be (A) 1 m/s (C) 5 m/s (B) 13 m/s (D) 10 m/s B-3. B-4. If speed of waer in river is 4 m/s and speed of swimmer wih respec o waer is 3 m/s, hen in which direcion he swimmer mus swim so ha he will reach direcly opposie end? (A) 17 wih direcion of river flow (B) 90 wih direcion of river flow (C) 143 wih direcion of river flow (D) Swimmer will never reach direcly opposie end A boa can go across a lake and reurn in ime 0 a a speed V. On a rough day here is uniform curren a speed u o help he onward journey and impede he reurn journey. If he ime aken o go across and reurn on he rough day be, hen / 0 = u (A) 1 V (B) 1 u 1- V u (C) 1 + V 1 (D) u 1+ V A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 3
B-5. o cross he river in shores disance, a swimmer should swim making angle q wih he upsream. Wha is he raio of he ime aken o swim across in he shores ime o ha in swimming across over shores disance. [Assume speed of swimmer in sill waer is greaer han he speed of river flow (A) cosq (B) sin q (C) an q (D) co q B-6. A man crosses he river perpendicular o river flow in ime seconds and ravels an equal disance down he sream in seconds. he raio of man s speed in sill waer o he speed of river waer will be: (A) - + (B) - + (C) + - (D) + - Secion : (C) Relaive moion in Rain and wind C-1. When a person walks on a sraigh road wih a speed 10 km/h, rain appears o fall vericlly downward. As he sops, he rain appears o fall a an angle 30º wih verical. he speed of rain wih respec o he person. (A) 0 km/hr (B) 10 3 km/hr (C) 10 km/hr (D) 0 3 km/hr C-. An aeroplane is o go along sraigh line from A o B, and back again. he relaive speed wih respec o wind is V.. he wind blows perpendicular o line AB wih speed u. he disance beween A and B is l. he oal ime for he round rip is: l (A) V - v vl (B) V - v Vl (C) V v l (D) V + v C-3. A flag is mouned on a car moving due Norh wih velociy of 0 km/hr. Srong winds are blowing due Eas wih velociy of 0 km/hr. he flag will poin in direcion (A) Eas (B) Norh - Eas (C) Souh - Eas (D) Souh - Wes C-4. Rain is falling verically wih a speed of 0 ms 1 relaive o air. A person is running in he rain wih a velociy of 5 ms 1 and a wind is also blowing wih a speed of 15 ms 1 (boh owards eas). Find he angle wih he verical a which he person should hold his umbrella so ha he may no ge drenched. (A) an 1 - æ 1 ö (B) an 1 ç (C) an è 1 () (D) 45 ø C-5. A buerfly is flying wih velociy ˆ ˆ 10i + 1j m/s and wind is blowing along x axis wih velociy u. If buerfly sars moion from A and afer some ime reaches poin B, find he value of u. (A) m/s (B) 6 m/s (C) 4 m/s (D) 3m/s C-6. Raindrops are falling verically wih a velociy of 10 m/s. o a cyclis moving on a sraigh road he raindrops appear o be coming wih a velociy of 0 m/s. he velociy of cyclis is : (A) 10 m/s (B) 10 3 m/s (C) 0 m/s (D) 0 3 m/s A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 4
Secion : (D) Velociy of separaion & approach D-1. wo men P & Q are sanding a corners A & B of square ABCD of side 8 m. hey sar moving along he rack wih consan speed m/s and 10 m/s respecively. he ime when hey will mee for he firs ime, is equal o : (A) sec (B) 3 sec (C) 1 sec (D) 6 sec D-. r For wo paricles A and B, given ha A = î + 3 ĵ, r B is he value of x if hey collide. = 6 î + 7 ĵ, v r A = 3 î ĵ and v r B (A) 1 (B) 1 (C) (D) = x î 5 ĵ. Wha D-3. wo paricles A and B move wih velociies v 1 and v respecively along he x & y axis. he iniial separaion beween hem is d as shown in he fig. Find he leas disance beween hem during heir moion. d.v 1 (A) v1 + v d.v (B) v1 + v d.v 1 (C) v1 + v d.v (D) v1 + v D-4. P is a poin moving wih consan speed 10 m/s such ha is velociy vecor always mainains an angle 60 wih line OP as shown in figure (O is a fixed poin in space). he iniial disance beween O and P is 100 m. Afer wha ime shall P reach O. (A) 10 sec. (B) 15 sec. (C) 0 sec. (D) 0 3 sec A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 5
PAR - II : MISLLANEOUS QUESIONS COMPREHENSION YPE Comprehensions # 1 : wo paricles A and B are projeced in he verical plane wih same inial velociy u 0 from poin (0, 0) and (l, - h) owards each oher as shown in figure a = 0. 1. he pah of paricle A wih respec o paricle B will be : (A) parabola (B) sraigh line parallel o x - axis. (C) sraigh line parallel o y-axis (D) none of hese.. Minimum disance beween paricle A and B during moion will be : (A) l (B) h (C) l + b (D) l + h 3. he ime when separaion beween A and B is minimum is : (A) x u cos q 0 (B) h g (C) l u0 cos q l (D) u cos q 0 Comprehensions # : Raindrops are falling wih a velociy 10 m/s making an angle of 45 wih he verical. he drops appear o be falling verically o a man running wih consan velociy. he velociy of rain drops change such ha he rain drops now appear o be falling verically wih 3 imes he velociy i appeared earlier o he same person running wih same velociy. 4. he magniude of velociy of man wih respec o ground is : (A) 10 m/s (B) 10 3 m/s (C) 0 m/s (D) 10 m/s 5. Afer he velociy of rain drops change, he magniude of velociy of raindrops wih respec o ground is: (A) 0 m/s (B) 0 3 (C) 0 m/s (D) 10 3m/s 6. he angle (in degrees) beween he iniial and he final velociy vecors of he raindrops wih respec o he ground is : (A) 8 (B) 15 (C).5 (D) 37 A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 6
MACH HE COLUMN Mach he Column : 7. wo paricles A and B moving in x-y plane are a origin a = 0 sec. he iniial velociy vecors of A and B are u a A B = 8 ˆi m/s and ub = 8 ˆj m/s. he acceleraion of A and B are consan and are aa =- ˆi m/s and =- ˆj m/s. Column I gives cerian saemens regarding paricle A and B. Column II gives corresponding resuls. Mach he saemens in column I wih corresponding resuls in Column II. Columns I Column II (A) he ime (in seconds) a wich velociy (p) 16 of A relaive o B is zero (B) he disance (in meres) bewen A and B (q) 8 when heir relaive velociy is zero. (C) he ime (in seconds) afer = 0 sec. (r) 8 a which A and B are a same posiion (D) he magniude of relaive velociy of A and B (s) 4 a he insan hey are a same posiion. () 6 seconds PAR - I : MIXED OBJECIVE * Marked Quesions are having more han one correc opion. Single Correc Answer ype : 1. hree elephans A, B and C are moving along a sraigh line wih consan speed in same direcion as shown in figure. Speed of A is 5 m/s and speed of C is 10 m/s. Iniially separaion beween A & B is d and beween B & C is also d. When B caches C separaion beween A & C becomes 3d. hen he speed of B will be - (A) 7.5 m/s (B) 15 m/s (C) 0 m/s (D) 5 m/s. A projecile A is projeced from ground. An observer B running on ground wih uniform velociy of magniude v observes A o move along a sraigh line. he ime of fligh of A as measured by B is. hen he range R of projecile on ground is : (A) R = v (C) R > v (B) R < v (D) Informaion insufficien 3. A swimmer crosses a river wih minimum possible ime 10 second. And when he reaches he oher end sars swimming in he direcion owards he poin from where he sared swimming. Keeping he direcion fixed he swimmer crosses he river in 15 sec. he raio of speed of swimmer wih respec o waer and he speed of river flow is (Assume consan speed of river & swimmer) : (A) 3 (B) 4 9 (C) 5 (D) 5 A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 7
4. wo poins P and Q move in same plane such ha he relaive acceleraion of P wih respec o Q is zero. hey are moving such ha he disance beween hem is decreasing. Pick he correc saemen for P and Q o collide (A) he line joining P and Q should no roae. (B) he line joining P and Q should roae wih consan angular speed (C) he line joining P and Q should roae wih variable angular speed (D) All he above saemen are correc 5. Wind is blowing in he norh direcion a speed of m/s which causes he rain o fall a some angle wih he verical. Wih wha velociy should a cyclis drive so ha he rain appears verical o him : (A) m/s souh (B) m/s norh (C) 4 m/s wes (D) 4 m/s souh 6. A bucke is placed in he open where he rain is falling verically. If a wind begins o blow horizonally a double he velociy of he rain, how will be rae of filling of he bucke change? (A) Remain unchanged (B) Doubled (C) Halved (D) Become four imes Muliple Correc Answer(s) ype 7. A river is flowing wih a speed of 1 km/hr. A swimmer wans o go opoin C saring from A. he swims wih a speed of 5 km/hr, a angle q, w.r.. he river. If AB = BC = 400 m. hen : (A) he value of q is 53 (B) ime aken by he man is 6 min (C) ime aken by he man is 8 min (D) he value of q is 45 8. A ball is hrown verically upward (relaive o he rain) in a comparmen of a moving rain. (A) he ball will mainain he same horizonal velociy as ha of he person (or he comparmen) a he ime of hrowing. (B) If he rain is acceleraing hen he horizonal velociy of he ball will be differen from ha of he rain velociy, a he ime of hrowing. (C) If he ball appears o be moving backward o he person siing in he comparmen i means ha speed of he rain is increasing. (D) If he ball appears o be moving ahead of he person siing in he comparmen i means he rain's moion is rearding. 9. A swimmer who can swim in a river wih speed mv (wih respec o sill waer) where v is he velociy of river curren, jumps ino he river from one back o cross he river. (A) If m 1 he can no reach a poin on oher bank direcly opposie o his saring poin. (B) If m < 1 he can no cross he river. (C) If m > 1 he can reach a poin on oher bank. (D) He can reach he oher bank a some poin, whaever be he value of m. 10. wo sones are hrown verically upwards simulaneously from he same poin on he ground wih iniial speed u 1 = 30 m/sec and u = 50 m/sec. Which of he curve represens correc variaion (for he ime inerval in which boh reach he ground) of (x - x 1 ) = he relaive posiion of second sone wih respec o firs wih ime (). (v - v 1 ) = he relaive velociy of second sone wih respec o firs wih ime (). Assume ha sones do no rebound afer hiing : (A) (B) (C) (D) A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 8
PAR - II : SUBJECIVE QUESIONS 1. Men are running along a road a 15 km/h behind one anoher a equal inervals of 0 m. Cycliss are riding in he same direcion a 5 km/h a equal inervals of 30 m. A wha speed in km/h an observer ravelling along he road in opposie direcion so ha whenever he mees a runner he also mees a cyclis? (neglec he size of cycle). A paricle A is moving wih a consan velociy of 10 m/sec. Anoher paricle B is moving wih a consan bu unknown velociy. A an insan, he line joining A and B makes an angle of 30 wih velociy of A. Find he minimum possible magniude of velociy of B in m/s, if hey collide afer some ime. (see figure) A 30 B 3. A moorboa going down sream over come a floa a a poin M which is fixed wih respec o ground. 60 minues laer i urned back and afer some ime passed he floa a a disance of 6 km from he poin M. Find he velociy of he sream assuming a consan velociy for he moorboa in sill waer in km/h. PAR-I II-JEE (PREVIOUS YEARS PROBLEMS) * Marked Quesions are having more han one correc opion. 1. A river is flowing from wes o eas a a speed of 5 mere per minue. A man on he souh bank of he river, capable of swimming a 10 mere per minue in sill waer, wans o swim across he river in he shores ime. He should swim in a direcion : [ JEE-1983, 1 ] (A) due norh (B) 30 0 eas of norh (C) 30 0 wes of norh (D) 60 0 eas of norh. A boa which has a speed of 5 km/hr in sill waer crosses a river of widh 1 km along he shores possible pah in 15 minues. he velociy of he river waer in km/hr is : [ JEE-1988, ] (A) 1 (B) 3 (C) 4 (D) 41 3. An aeroplane is flying verically upwards wih a uniform speed of 500 m/s. When i is a a heigh of 1000 m above he ground a sho is fired a i wih a speed of 700 m/s from a poin direcly below i. Wha should be he uniform acceleraion of he aeroplane now so ha i may escape from being hi? (g = 10 m/s ) [ REE-1994, 6 ] 4. he widh of a river is 5 m and in i waer is flowing wih a velociy of 4 m/min. A boaman is sanding on he bank of he river. He wans o sail he boa o a poin a he oher bank which is direcly opposie o him. In wha ime will he cross he river, if he can sail he boa a 8 m/min, relaive o he waer. [ REE-1995, 6 ] 5. wo guns siuaed on he op of a hill of heigh 10m fire one sho each wih he same speed 5 3 m/s a some inerval of ime. One gun fires horizonaly and oher fires upwards a an angle of 60º wih he horizonal. he shos collide in air a poin P. Find : [ JEE '96, 5 ] (a) he ime inerval beween he firings and (b) he coordinaes of he poin P. ake origin of he coordinae sysem a he foo of he hill righ below he muzzle and rajecories in x-y plane A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 9
6. A large heavy box is sliding wihou fricion down a smooh plane of inclinaion q From a poin P on he boom of he box, he iniial speed of he paricle wih respec o he box is u and he direcion of projecion makes an angle a wih he boom as shown in he figure : q P a Q (a) Find he disance along he boom of he box beween he poin of projecion P and he poin Q where he paricle lands ( Assume ha he paricle does no hi any oher surface of he box. Neglec air resisance.) [JEE-1998, 5 + 3/10] (b) If he horizonal displacemen of he paricle as seen by an observer on he ground is zero, find he speed of he box wih respec o he ground a he insan when he paricle was projeced. 7. An objec A is kep fixed a he poin x = 3 m and y = 1.5 m on a plank P raised above he ground. A ime = 0 he plank sars moving along he + x direcion wih an acceleraion 1.5 m/s. A he same insan a sone is projeced from he origin wih a velociy u r as shown. A saionary person on he ground observes he sone hiing he objec during is downward moion a an angle of 45 0 o he horizonal. All he moions are in X Y plane. Find u r and he ime afer which he sone his he objec. ake g = 10 m/s. [JEE-000 (Mains) 5 + 3/100 ] 8. On a fricionless horizonal surface, assumed o be he x - y plane a small rolley A is moving along a sraigh line parallel o he y - axis as shown in he figure wih a consan velociy of ( 3 1) m/s. A a paricular insan, when he line OA makes an angle of 45º wih he x - axis, a ball is hrown along he surface from he origin O. Is velociy makes an angle f wih he x - axis when i his he rolley. (a) he moion of he ball is observed from he frame of he rolley. Calculae he angle q made by he velociy of he ball wih he x - axis in his frame. (b) Find he speed of he ball wih respec o he surface, if f = 4 q/3. [ JEE 00, + 3/60 ] A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 10
9. SAEMEN -1 [JEE' 008, 3/163 ] For an observer looking ou hrough he window of a fas moving rain, he nearby objecs appear o move in he opposie direcion o he rain, while he disan objecs appear o be saionary. and SAEMEN - If he observer and he objec are moving a velociies V r and 1 V r respecively wih reference o a laboraory r r frame, he velociy of he objec wih respec o he observer is V - V1. (A) SAEMEN -1 is rue, SAEMEN - is rue; SAEMEN - is a correc explanaion for SAEMEN -1 (B) SAEMEN -1 is rue, SAEMEN - is rue; SAEMEN - is NO a correc explanaion for SAEMEN -1 (C) SAEMEN -1 is rue, SAEMEN - is False (D) SAEMEN -1 is False, SAEMEN - is rue. PAR-II AIEEE (PREVIOUS YEARS PROBLEMS) * Marked Quesions are having more han one correc opion. 1. A body is a res a x = 0. A = 0, i sars moving in he posiive x-direcion wih a consan acceleraion. A he same insan anoher body passes hrough x = 0 moving in he posiive x-direcion wih a consan speed. he posiion of he firs body is given by x1() afer ime and ha of second body by x() afer he same ime inerval. Which of he following graphs correcly describes (x1 x) as a funcion of ime? [AIEEE 008] (1) () (3) (4). wo fixed fricionless inclined planes making an angle 30º and 60º wih he verical are shown in he figure. wo blocks A and B are placed on he wo planes. Wha is he relaive verical acceleraion of A wih respec o B? [AIEEE 010, 4/144] (1) 4.9 ms in horizonal direcion () 9.8 ms in verical direcion (3) Zero (4) 4.9 ms in verical direcion A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 11
NCER QUESIONS 1. A je airplane ravelling a he speed of 500 km h 1 ejecs is producs of combusion a he speed of 1500 km h 1 relaive o he je plane. Wha is he speed of he laer wih respec o an observer on he ground?. wo rains A and B of lengh 400 m each are moving on wo parallel racks wih a uniform speed of 7 km h 1 in he same direcion, wih A ahead of B. he driver of B decides o overake A and acceleraes by 1 m s. If afer 50 s, he guard of B jus brushes pas he driver of A, wha was he original disance beween hem? 3. On a wo-lane road, car A is ravelling wih a speed of 36 km h 1. wo cars B and C approach car A in opposie direcions wih a speed of 54 km h 1 each. A a cerain insan, when he disance AB is equal o AC, boh being 1 km, B decides o overake A before C does. Wha minimum acceleraion of car B is required o avoid an acciden? 4. wo owns A and B are conneced by a regular bus service wih a bus leaving in eiher direcion every minues. A man cycling wih a speed of 0 km h 1 in he direcion A o B noices ha a bus goes pas him every 18 min in he direcion of his moion, and every 6 min in he opposie direcion. Wha is he period of he bus service and wih wha speed (assumed consan) do he buses ply on he road? 5. On a long horizonally moving bel (Fig.), a child runs o and fro wih a speed 9 km h 1 (wih respec o he bel) beween his faher and moher locaed 50 m apar on he moving bel. he bel moves wih a speed of 4 km h 1. For an observer on a saionary plaform ouside, wha is he (a) speed of he child running in he direcion of moion of he bel?. (b) speed of he child running opposie o he direcion of moion of he bel? (c) ime aken by he child in (a) and (b)? Which of he answers aler if moion is viewed by one of he parens? 6. A man can swim wih a speed of 4.0 km/h in sill waer. How long does he ake o cross a river 1.0 km wide if he river flows seadily a 3.0 km/h and he makes his srokes normal o he river curren? How far down he river does he go when he reaches he oher bank? 7. In a harbour, wind is blowing a he speed of 7 km/h and he flag on he mas of a boa anchored in he harbour fluers along he N-E direcion. If he boa sars moving a a speed of 51 km/h o he norh, wha is he direcion of he flag on he mas of he boa? A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 1
Exercise # 1 PAR-I A-1. (C) A-. (D) A-3. (D) A-4. (D) A-5. (A) A-6. (C) A-7. (B) A-8. (D) A-9. (C) A-10. (B) A-11. (D) B-1. (B) B-. (B) B-3. (D) B-4. (B) B-5. (B) B-6. (C) C-1. (B) C-. (A) C-3. (C) C-4. (B) C-5. C-6. (B) D-1. (B) D-. (B) D-3. (C) D-4. (C) PAR-II 1. (B). (B) 3. (C) 4. (D) 5. (A) 6. (B) 7. (A) s ; (B) p ; (C) r ; (D) q Exercise # PAR-I 1. (B). (A) 3. (C) 4. (A) 5. (B) 6. (A) 7. (AB) 8. (ACD) 9. (AD) 10. (AD) 1. 5. 5 3. 3 PAR-II Exercise # 3 PAR-I 5 1. (A). (B) 3. a > 10 m/s 4. = 8-4 18 minue 5 5. (a) 1s, (b) ( 5 3 m. 5 m ) 6. (a) PQ = (u sin a )/ g cos q, (b) V = u cos( a + q) (down he plane) cosq 15 5 7. ( 4 î + ĵ ) m/s ; 1 second 8. (a) q = 45º ; (b) m/s 9. (B) 4 1. (). (4) PAR-II Exercise # 4 1. 1000 Km/h. 150 m 3. 1 ms 4. = 9 min., Speed = 400 km/h. 5. (a) 13 km h 1 ; (b) 5 km h 1 ; (c) 0 second in eiher direcion, viewed by any one of he parens, he speed of he child is 9 km h 1 in eiher direcion ; answer o c is unalered. 6. 15 min, 750 m 7. Eas (approximaely) A-479 Indra Vihar, Koa Rajashan 34005 Page No. # 13