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Particle bouncing between walls

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Homework Statement
A particle is situated between two walls that are closing in on each other. The particle is moving at 1.61 km/s in the -x direction, the left wall is moving at 1.01 km/s in the +x direction, and the right wall is moving at 2.51 km/s in the -x direction. What is the velocity of the particle after bouncing off of the left wall 10 times and the right wall 9 times?
Homework Equations
Delta v = v final - v initial

Conservation of momentum

???
I thought it would be a good idea to pretend that the walls are stationary and that each time the particle hits a wall, it gets a velocity addition of the velocity of the wall it’s hitting. Using this I ended up at the formula

V = initial velocity of particle + n(velocity of left wall) + m(velocity of right wall)

where n and m are the number of collisions with the left and right walls, respectively.

Needless to say, this does not give me the right answer. Thoughts?
 
Last edited:

Orodruin

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Assuming that the collisions with the walls are elastic, what happens with the velocity of the ball after collision with a moving wall?
 
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Assuming that the collisions with the walls are elastic, what happens with the velocity of the ball after collision with a moving wall?
Would you add twice the magnitude of the initial velocity to the initial velocity?
 

Orodruin

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Would you add twice the magnitude of the initial velocity to the initial velocity?
What happens in the rest frame of the wall? What does that mean for a different frame?
 

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