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Question

A boy sitting at the rear end of a railway compartment of a train, running at a constant acceleration on horizontal rails, throws a ball towards the fore end of the compartment with velocity 20 m/s (relative to train) at an angle 370 above the horizontal , when the train is running at speed of 10 m/s. If same boy catches the ball without moving from seat and at the same height of projection. Then find the speed of train (in m/s) at the instant of his catching the ball. (Here g = 10m/s2; sin370=3/5).

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Solution

Velocity of ball w.r.t boy =20 m/s

Horizontal velocity of the ball with respect to ground =20cos37+10=26 m/s

Vertical velocity of the ball with respect to ground =20sin37=12 m/s

Time of flight =2×12g=125 sec

Distance traveled by ball w.r.t ground =26×125

Distance covered by train, s=ut+12at2

26t=10t+12at2

16=12at

at=32

But v=u+at

So, v=10+32=42 m/s

Therefore speed of train at the instant of his catching the ball is 42 m/s.

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