Question

PSLV launches a rocket in a gravity free space with constant acceleration $5{\text{m/s}}^2$ along +x direction (see figure). The length of the chamber inside the rocket is $6\text{m}$. At time $t=0$, a ball is thrown from the left end of the chamber in +x direction with a speed $0.7\text{m/s}$ relative to the rocket. At the same time, another ball is thrown in opposite direction to the previous ball with a speed $0.3\text{m/s}$ relative to the rocket. The time in seconds when the two balls hit each other is

Answer 1

Given that
$u_A=0.7\text{m/s};u_B=0.3\text{m/s}$
$a=5{\text{m/s}}^2;l=6\text{m}$

Let $t$ be the time at which both balls hit each other.

At time $t$,
Relative distance covered by ball A $S_{rel}=6\text{m}$
Relative velocity of ball A w.r.t ball b $u_{rel}=0.7+0.3=1\text{m/s}$
Relative acceleration, $a_{rel}=0$
[since both the balls are inside rocket chamber, moving with the same acceleration]

Using formula,
$S_{re}=u_{rel}\times t$
$\Rightarrow t=\frac{S_{rel}}{u_{rel}}-----\left(1\right)$
$\Rightarrow t=\frac{6}{1}=6\text{s}$
is the time when the two balls hit each other.