Question

A rocket is moving in a gravity free space with a constant acceleration of $2{ms}^{-2}$ 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 $0.3{ms}^{-1}$ relative to the rocket. At the same time, another ball is thrown in $-x$ direction with a speed of $0.2{ms}^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is:

Answer 1

Rocket has acceleration in the direction left ball hence for right ball acceleration of left ball is $-2m{s}^{-2}$ and for left ball acceleration of right ball is $2m{s}^{-1}$.

assuming when they hit each other the displacement of right ball is $S$. $\therefore$ displacement of left ball is $4-S$. because length of rocket is $4m$.

for right ball,

$S=0.3t-\left(1/2\right)\times 2t^2$

for left ball,

$4-S=0.2t+\left(1/2\right)\times 2t^2$

equating both the equations we get,

$t=8sec$