Question

A rocket is moving in a gravity free space with a constnat acceleration of `2ms^(-1)` along +x direction (see Fig.5.126). The length of a chamber inside the rocket is 4m. A ball is thrown from th left end of the chamber in +x direction with a speed of 0.3 `ms^(-1)` relaitve to the rocket. At the same time , another ball is thrown in -x direction with a speed of 0.2ms^(-1)` from its right and relative to the rocket. the time in seconds when the two balls hit each other is:

Answer 1

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) + (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) + (1)/(2) a_(2) t_(2)^(2)`
` 4 - x = 0.2 t + t^(2)` ....(2)
From `(1)` and `(2) t = 8 sec`