Part 3-Motion in a straight line hard

A ball is dropped from top of a tower of height 'h'. It takes time 'T' to reach ground. What is height of the body from ground at time 'T/4' ?

A particle moves with an initial velocity v₀ and retardation kv, where v is the velocity at any time t.

An aeroplane is flying vertically upwards with a uniform speed of 500 m/s. When it is at a height of 1000 m above the ground a shot is fired at it with a speed of 700 m/s from a point directly below it. The minimum uniform acceleration of the aeroplane now so that it may escape from being hit ? (g = 10 m/s²)

A stone is thrown upwards from a tower with a velocity 50 ms^–1. Another stone is simultaneously thrown downwards from the same location with a velocity 50 ms^–1. When the first stone is at the highest point, the relative velocity of the second stone with respect to the first stone is (assume that second stone has not yet reached the ground)  :

A thief is running away on a straight road with a speed of 9 ms^–1. A police man chases him on a jeep moving at a speed of 10 ms^–1. If the instantaneous separation of the jeep from the motorcycle is 100m, how long will it take for the police man to catch the thief?

Two trains A and B which are 100 km apart are travelling towards each other on different tracks with each having initial speed of 50 km/h . The train A accelerates at 20 km/h² and the train B retards at the rate 20 km/h². The distance covered by the train A when they cross each other is :

A jet airplane travelling from east to west at a speed of 500 km h^–1 eject out gases of combustion at a speed of 1500 km h^–1 with respect to the jet plane. What is the velocity of the gases with respect to an observer on the ground ?

A helicopter is flying south with a speed of 50 kmh^–1. A train is moving with the same speed towards east. The relative velocity of the helicopter as seen by the passengers in the train will be towards.

Two particles are moving with velocities v₁ and v₂. Their relative velocity is the maximum, when the angle between their velocities is :

Two billiard balls are rolling on a flat table. One has velocity components v_x = 1m/s, v_y = √3m/s and the other has components v_x = 2m/s and v_y = 2 m/s. If both the balls start moving from the same point, the angle between their path is –

To cross the river in shortest distance, a swimmer should swim making angle θ with the upstream. What is the ratio of the time taken to swim across in the shortest time to that in swimming across over shortest distance. [Assume speed of swimmer in still water is greater than the speed of river flow]

An airplane pilot sets a compass course due west and maintains an air speed of 240 km/h. After flying for 1/2h, he finds himself over a town that is 150 km west and 40 km south of his starting point. The wind velocity (with respect to ground) is :

It is raining vertically downwards with a velocity of 3 km h^–1 . A man walks in the rain with a velocity of 4 kmh^–1. The rain drops will fall on the man with a relative velocity of :

A man walks in rain with a velocity of 5 kmh^–1. The rain drops strike at him at an angle of 45° with the horizontal. The velocity of the rain if it is falling vertically downward is :

Raindrops are falling vertically with a velocity of 10 m/s. To a cyclist moving on a straight road the raindrops appear to be coming with a velocity of 20 m/s. The velocity of cyclist is :

A person standing on the escalator takes time t₁ to reach the top of a tower when the escalator is moving. He takes time t₂ to reach the top of the tower when the escalator is standing. How long will he take if he walks up on a moving escalator?

Two cars are moving in the same direction with a speed of 30 km h^–1. They are separated from each other by 5 km. Third car moving in the opposite direction meets the two cars after an interval of 4 minutes. What is the speed of the third car?

A bus is moving with a velocity 10 ms^–1 on a straight road. A scooterist wishes to overtake the bus in 100s. If, the bus is at a distance of 1 km from the scooterist, with what velocity should the scooterist chase the bus? (Neglect size of the bus)

A body is thrown up in a lift with a velocity u relative to the lift and the time of flight is found to be ‘t‘. The acceleration with which the lift is moving up is :

A coin is released inside a lift at a height of 2 m from the floor of the lift. The height of the lift is
10 m. The lift is moving with an acceleration of 11 m/s² The time after which the coin will strike with the lift is :

A particle is thrown up inside a stationary lift of sufficient height. The time of flight is T. Now it is thrown again with same initial speed v₀ with respect to lift. At the time of second throw, lift is moving up with speed v₀ and uniform acceleration g upward (the acceleration due to gravity). The new time of flight is–