Question

A rocket is moving in a gravity free space with a constant acceleration of $2m/s^2$ along $+x$ direction (see figure). The length of a chamber inside the rocket is $4m$. A ball is thrown from the left end of the chamber in $+x$ direction with a speed of $0.3m/s$ relative to the rocket. At the same time, another ball is thrown in $–x$ direction with a speed of $0.2m/s$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is

Answer 1

$S_1=0.2t+\frac{1}{2}\times 2\times t^2$
$S_2=0.3t-\frac{1}{2}\times 2\times t^2$
$s_1+s_2=4$
$0.5t=4$
$t=8$

Alternate



Assuming closed chamber the collision will be very dosed to the left end. Hence, time taken by ball B to reach left end will be given by

$4=\left(0.2\right)\left(t\right)+\frac{1}{2}\left(2\right)(t{)}^2$
$\Rightarrow t\approx 2s$