A rocket is moving in a gravity free space with a constant acceleration of 2 m/s2 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 ?
The answer ranges from 0 to 9.
The Attempt at a Solution
Here is what I did.
If rocket accelerates by 2 m/s2 in +x direction, then balls inside it also accelerates with it with same value and in same direction in ground frame. Thus when we switch to frame of the rocket there is no acceleration on balls. Inside that frame I impose the concept of relative velocity and convert this two body problem to one body.
Velocity of left ball relative to right ball = 0.5 m/s in +x direction.
Thus time taken to collide = distance/Velocity of left ball relative to right ball = 4/0.5=8 seconds.
This is the correct answer.
However exam in which this question was asked says that both 8 seconds and 2 seconds answers are acceptable.
One book offers solution as :
Maximum displacement of the left ball from the left wall of the chamber is 2.25 cm, so the right ball has to travel almost the whole length of the chamber (4m) to hit the left ball. So the time taken by the right ball is 1.9 sec (approximately 2 sec).
Now my doubt is as follows :
How is 2 seconds a correct answer ? Also how can there be "two" values of time of collision ?
Please help !!
Thanks in advance... :)