A boy sitting at the rear end of a railway compartment of a train, running at a constant acceleration on horizontal rails throws towards the fore end of the compartment with a muzzle velocity of 20 m/

Question

A boy sitting at the rear end of a railway compartment of a train, running at a constant acceleration on horizontal rails throws towards the fore end of the compartment with a muzzle velocity of 20 m/sec at an angle 37° above the horizontal, when the train is running at a speed of 10 m/sec. If the same boy catches the ball without moving from his seat and at the same height of projection, find the speed of the train at the instant of his catching the ball.

TestHub · Accepted Answer

The ball's horizontal velocity (ground frame) is
$10 + 20 cos 3 7^{\circ} = 26 m / s$ ;
the boy starts at 10 m/s and accelerates at $a$ . Equal displacement at the catch:
$10 t + \frac{1}{2} a t^{2} = 26 t$ ,
so
$a t = 32 m / s$
and the train's speed then is
$10 + 32 = 42 m / s \approx 41.99 m / sec$ .
Matches the printed answer (the flight time
$t = \frac{2 \times 20 sin 3 7 ^{\circ}}{9.8} = 2.45$
s fixes
$a = 13.1 m / s^{2}$ ,
though the final speed needs only $a t$ ).

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