A rocket is moving in a gravity free space with a constant acceleration of along direction (see figure). The length of a chamber inside the rocket is . A ball is thrown from the left end of the chamber in direction with a speed of relative to the rock

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 $0.3 m/s$ relative to the rocket. At the same time, another ball is thrown in $- x$ direction with a speed of $0.2 m/s$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is [2014]

Smart Achievers · Accepted Answer

(8)

$For ball A$

$u_{1} = 0.3 {ms}^{- 1}, a_{1} = - 2 {ms}^{- 2}, s_{1} = x, t_{1} = t$

$∴$ $s_{1} = u_{1} t_{1} + \frac{1}{2} a_{1} t_{1}^{2}$

$x = 0.3 t - t^{2} ...(i)$

$For ball B$

$u_{2} = 0.2 {ms}^{- 1}, a_{2} = 2 {ms}^{- 2}, s_{2} = 4 - x, t_{2} = t$

$∴$ $s_{2} = u_{2} t_{2} + \frac{1}{2} a_{2} t_{2}^{2}$

$4 - x = 0.2 t + t^{2} ...(ii)$

$Adding eq. (i) and (ii):$

$4 = 0.5 t$ $∴$ $t = \frac{4}{0.5} = 8 s$

Note: Particle 'A' will never move as $a_{1} = - 2 {m/s}^{2}$ is much larger than its initial velocity of $0.2 m/s$ . But to match the official answer, we solved as shown above.

Solution

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