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 ${37}^0$ 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 = 10$m/s^2$; $sin{37}^0=3/5$).

Answer 1

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

Horizontal velocity of the ball with respect to ground $=20\cos 37+10=26m/s$

Vertical velocity of the ball with respect to ground $=20\sin 37=12m/s$

Time of flight $=\frac{2\times 12}{g}=\frac{12}{5}sec$

Distance traveled by ball w.r.t ground $=26\times \frac{12}{5}$

Distance covered by train, $s=ut+\frac{1}{2}a{t}^2$

$26t=10t+\frac{1}{2}a{t}^2$

$16=\frac{1}{2}at$

$at=32$

But $v=u+at$

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

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