Kinematics Rocket Question

  • #26
130
13
Nope. It is a 3 body problem. If you see from rocket frame you are bringing rocket "virtually" to rest and this imposes acceleration of 2 m/s2 on each of the ball in -x direction.
You can do nothing more than that. You seem to be thinking that we find relative velocity of one ball w.r.t another. Albeit, that doesn't mean that you ignore acceleration of rocket.
You can't convert this 3 body problem to one body.

The acceleration of the rocket doesn't matter when collisions aren't assumed to happen. Just see one ball w.r.t. the other. Answer is 8 sec only.

You can solve it from the rocket frame if you like, you will get the same answer.
 
  • #27
785
15
The acceleration of the rocket doesn't matter when collisions aren't assumed to happen. Just see one ball w.r.t. the other. Answer is 8 sec only.

You can solve it from the rocket frame if you like, you will get the same answer.

Well well. I did get 8 seconds from both the frames only if rocket is infinitely long. But then I have my apprehensions :


1. The question specifically stated that the chamber length between two balls is 4 m.

2. The question was so framed that even a gauche would have implicitly assumed that collision has to occur.

So how in the world had they (the paper setters) stated that 8 seconds is also the correct answer ?

There has to be some way..

Maybe someone else will feel free to chip in.. :smile: He/she may enlighten me or.... I have to confess that question created by IIT is wrong. -_- Heck :P

Anyone else ?
 
  • #28
ehild
Homework Helper
15,543
1,914
Now why exam accepted 8 s ?

That's my reasoning :

If the balls are "kept on the floor of rocket cabin", then they have the same acceleration as rocket. Hence from rocket frame 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.

Only when the balls are fixed to the floor would they move with the same acceleration as the rocket. But then they do not move with respect to the rocket, and never meet.

The 8 s is a possible solution if the back wall of the rocket opens after the first ball leaves it.
The ball travels forward, but decelerates with respect to the rocket. Its relative velocity becomes zero, and then it starts to move backwards. If the wall is no more present it goes on backwards just like the other ball which overcomes it in 8 s.


ehild
 
  • #29
785
15
Only when the balls are fixed to the floor would they move with the same acceleration as the rocket. But then they do not move with respect to the rocket, and never meet.

The 8 s is a possible solution if the back wall of the rocket opens after the first ball leaves it.
The ball travels forward, but decelerates with respect to the rocket. Its relative velocity becomes zero, and then it starts to move backwards. If the wall is no more present it goes on backwards just like the other ball which overcomes it in 8 s.


ehild

Thanks ehild ! :)

I expected that. Although the question stated that chamber length is 4 m, none would have though of assuming that the wall of rocket chamber is absent.

Anyway comments and views shall be greatly acknowledged. Thanks to all once again!
 

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