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Relative Velocity

A rocket is m...

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 is

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Solution

From the reference frame of the rocket the magnitude of the relative velocity of one of the ball
with respect to other is $(0.2 + 0.3) = 0.5 m / s$
So time taken $=$ $\frac{R e l a t i v e S e p a r a t i o n}{R e l a t i v e v e l o c i t y} = \frac{4}{0.5} = 8 s$

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