A rocket is moving in a gravity free space with a constant acceleration of 2 m s - 2 along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in + x direction with a speed of 0.3 m s - 1 relative to the rocket. At the…

Question

A rocket is moving in a gravity free space with a constant acceleration of $2 m s^{- 2}$ along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in + x direction with a speed of $0.3 m s^{- 1}$ relative to the rocket. At the same time, another ball is thrown in - x direction with a speed of $0.2 m s^{- 1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other for the first time is

Aicharya · Accepted Answer

Consider motion of two balls with respect to rocket. $\frac{u^2}{2 a}=\frac{0.3 \times 0.3}{2 \times 2}=\frac{0.09}{4}=0.02 m$ So, collision of two bals will take place very near to left wall. $\begin{aligned} & \text{for } B_{S}=ut+\frac{1}{2} a t^{2} \ & -4=-0.2 t\left(\frac{1}{2}\right) 2 t^{2} \Rightarrow t^{2}+0.2 t \ & -4=0 \ & \Rightarrow f t=\frac{-0.2 \pm \sqrt{0.04+16}}{2}=1.9 \end{aligned}$ nearest integer $=2 \mathrm{~s}$

A rocket is moving in a gravity free space with a constant acceleration of 2 m s - 2 along + x direction…

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