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RELATIVE MOTION, , velocity of A with respect to B will be equal to: (in km/hr), ., , Relative motion type 1, Velocity of A w.r.t B, , vA, , B, , = vA, , Realize, , C, , _ v, B, , C, , aA→B=aA →C -aB →C, , One dimensional chase, , Separation/collision Problems in single, line extend up to 2D 3D, , Distance of closest approach in, 2D 3D, Example –Chase, aiming other, , Uniform, , 1D,2D,3D relative, velocity, Example – Rain problems, , Single choice questions (Level0), 1A man walking at a rate 3km/h, the rain appears to fall, vertically downwards. When the man increase his speed to, 6km/h, it appears to fall at an angle of 45 0 with the, vertical. The real speed of the rain w.r.t earth is in km/h. ., (a) 2 3, (b) 3 2, (c) 3, (d) 2, 2. A ball is thrown vertically upward with a velocity, , ,, u from the balloon descending with velocity V. The, ball will pass by the balloon after time(a), , uv, uv, (b), 2g, 2g, , (c), , 2u  v , 2u  v , (d), g, g, , 3. A car A is going north east at 80 kmh-1 and another car B is, going south east with a velocity of 60 kmh-1. The, Velocity of A relative to B makes an angle with the north, equal to:, (a) tan-1 (2/7), (b) tan -1 (7/2), -1, (c) tan (7), (d) tan-1 (1/7), 4.Two cars A and B at rest at same point initially., If A starts with uniform velocity of 40 m/sec and, B starts in the same direction with constant, acceleration of 4m/s2, then B will catch A after, how much time, (a) 10 sec (b) 20 sec (c) 30 sec, (d) 35 sec, 5.Two motor cars A are B start simultaneously from same, point on two straight roads inclined at 60 0 to one another, with velocities of 30 and 40 km/hr respectively. The, , (a)10 3, (b) 10 13, (c) 15 13 (d) 5 3, 6. Rain, pouring down at an angle α with the vertical has a, speed of 10 ms-1. A girl runs against the rain with a speed, of 8 ms-1 and sees that the rain makes an angle β with the, vertical, then relation between α and β is:, (a) tan α = (8+10sinβ)/10cosβ, (b) tan β = (8+10sinα)/10cosα, (c) tan α =tan β, (d) tan α = cot β, 7. A train is moving towards east and a car is along, north, both with same speed. The observed, direction of car to the passenger in the train is, (a) East-north direction (b) West-north direction, (c) South-east direction (d) None of these, 8. Rain is falling vertically with a speed of 4m/s. after some, time, wind starts blowing with a speed of 3m/s in the north, to south direction. In order to protect himself from rain, a, man standing on the ground should hold his umbrella at an, angle  given by ., (a) tan-1(3/4) with the vertical towards south., (b) tan-1(3/4) with the vertical towards north., (c) cot-1(3/4) with the vertical towards south., (d) cot-1(3/4) with the vertical towards north., 9. Wind is blowing from the south at 10 ms-1 but to a cyclist it, appears to be blowing from the east at 10 ms-1. The cyclist has, a velocity:, (a) 10 iˆ - 10, , ĵ, , (c) -10 iˆ + 10, , (b) 10 iˆ + 10, , ĵ, , (d) -10 iˆ - 10 ĵ, ĵ, 10 Two trains, each 50 m long are travelling in, opposite direction with velocity 10m/s and, 15m/s. The time of crossing is, (a) 2s, (b) 4s, (c) 2 3 s, (d) 4 3 s, 11. A 120 m long train is moving in a direction with, speed 20m/s. A train B moving with 30m/s in, the opposite direction and 130 m long crosses, the first train in a time, (a) 6s, (b) 36s, (c) 38s (d) None of these

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12. A 210 meter long train is moving due north at a, speed of 25m/s. A small bird is flying due south, a little above the train with speed 5m/s. The time, taken by the bird to cross the train is, (a) 6s, (b) 7s, (c) 9s, (d) 10s, 13. A train of 150 meter length is going towards, north direction at a speed of 10m/s. A parrot, flies at a speed of 5m/s towards south direction, parallel to the railway track. The time taken by, the parrot to cross the train is, (a) 12sec, (b) 8sec, (c) 15sec, (d) 10sec, 14. The distance between two particles is decreasing, at the rate of 6m/s. If these particles travel with, same speed and in the same direction, then the, separation increase at the rate of 4m/s. The, particles have speeds as, (a) 5m/s ; 1m/s, (b) 4m/s ; 1m/s, (c) 4m/s ; 2m/s, (d) 5m/s ; 2m/s, , Relative motion type 2, , 15. A bus is moving with a speed of 10 ms-1 on a straight, road. A scooterist wishes to overtake the bus in 100, s. If the bus is at a distance of 1 km from the, scooterist, with what speed should the scooterist, chase the bus ?, (a) 40 ms-1 (b) 25 ms-1 (c) 10 ms-1 (d) 20 ms-1, , Single choice questions (Level 0), 19. A boat is traveling upstream with a velocity 4m/s w.r.t, river. The river flow velocity is 3m/s. A child start, walking from the rear towards the front of the boat with a, speed of 10m/s w.r.t earth. If the length of the boat is 2m, then the time in which the child reaches the front edge is. ., (a) 2/3sec (b) 2sec, (c) 2/9sec, (d) 1/9sec, 20.A boat is sent across a river with a velocity of 8, km/hr. If the resultant velocity of boat is 10 km/hr,, the velocity of the river is, (a) 10 km/hr (b) 8 km/hr (c) 6 km/hr (d) 4 km/hr, 21.A police jeep is chasing with, velocity of 45 km/h a thief, in another jeep moving with velocity 153 km/h. Police, fires a bullet with muzzle velocity of 180 m/s. The, velocity it will strike the car of the thief is, (a) 150m/s (b) 27m/s (c) 450m/s (d) 250m/s, 22.A boat moves with a speed of 5 km/h relative to, water in a river flowing with a speed of 3 km/h, and having a width of 1 km. The time, taken around a round trip is, (a) 5min (b) 60min, (c) 20min, (d) 30min, 23.A river is flowing from west to east at a speed of 5, m/minute. A man of the south bank of the river, capable of, swimming at 10 m/minute in still water, wants to swim the, river in the shortest time. He should swim in a direction:, (a) Due north, (b) 300 east of north, 0, (c) 30 west of north, (d) 600 east of north, Level 1, 24. A man rows directly across a flowing river in time t 1 and, rows an equal distance down the stream in time t 2. If u be, the speed of the man in still water and v be the speed of, the water show that:, , Accelerated relative motion, , 16. A express train is moving with a velocity v1. Its, driver finds another train is moving on the same, track in the same direction with velocity v2. To, escape collision, driver applies a retardation a on, the train. The minimum time of escaping, collision will be, v 2  v 22, v  v2, (a) t = 1, (b) t1 = 1, (c) None(d) Both, 2, a, 17. Two cars A and B at rest at same point initially., If A starts with uniform velocity of 40 m/sec and, B starts in the same direction with constant, acceleration of 4m/s2, then B will catch A after, how much time, (a) 10 sec (b) 20 sec (c) 30 sec (d) 35 sec, 18. Two particles A and B connected by a rigid rod AB., The rod slides along perpendicular rails as shown, here. The velocity of A to the left is 10 m/s. What is, the velocity of B when angle  = 60o ?, , ( a) t1:t2 =, , (u  v) : (u  v), , (b) t1:t2 =, , (u  v) : (u  v), , (c) t1:t2 = u  v : u  v (d) t1:t2 = (u  v) : (u  v), 25. Two trains whose lengths are 130 m and 110 m are moving, in opposite directions on parallel lines, the velocity of the, first being double that of the second. They are observed to, pass each other completely in 4 seconds. Find the velocity, of each., (a) 40m/s; 20m/s, (b) 20m/s; 60m/s, (c) 40m/seach, (d) 30 each, 2, , (a) 5.8 m/s (b) 9.8 m/s (c) 10 m/s, , [CBSE 1998], (d) 17.3 m/s, , 2

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26. A boat is moving with velocity of 3 iˆ  4 ˆj in, river and water is moving with a velocity of –, 3 iˆ -4 ĵ with respect to ground.Relative velocity, of boat with respect to groound is, (a) -6 iˆ -8 ĵ (b) 6 iˆ +8 ĵ (c) 8 iˆ, (d) 6 iˆ, 27., , 28., , A person swims in a river aiming to reach exactly, opposite point on the bank of a river. His speed of, swimming is 0.5 m/s at an angle 120o with the, direction of flow of water. The speed of water in, stream is, (a) 1.0 m/s (b) 0.5 m/s (c) 0.25 m/s (d) 0.43 m/s, A boat which has a speed of 5 km/hr in still water, crosses a river of width 1 km along the shortest, possible path in 15 minutes. The velocity of the, river water in km/hr is, (a) 3, , (d) 1, 21, 29. An aeroplane flies in the east direction from A to B. The, velocity of the aeroplane with respect to the wind is V and, the velocity of wind with respect to earth is U. The, distance between A & B is L. If the wind is blowing in the, north direction, Show that the time taken by the aero plane, to complete one tip from A to B then back to is, (a) (2L/V)/(1-U/V) ., (b) (2L/V)/(1-U/V)1/2 ., 2, 2 1/2, (c) (2L/V)/(1-U /V ) ., (d) (4L/V)/(1-U2/V2)1/2, 30.Two men M and N starts swimming from the same point on, the, river, with, velocity, vector, given, as, , , , , VM E, , (b) 4, , (c), , , ,  2iˆ VN R  3iˆ  2 ˆj and VM R  4iˆ  6 ˆj, , If M and N starts swimming at the same time then the, separation between them after 4 sec is., (a), , 130 m (b) 2 65 m (c) 3 65 m (d) N.O.T., , .. by Praveen gupta