Particle bouncing between walls

[Josh0768]

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?

Relevant 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?

 

[Orodruin]

Assuming that the collisions with the walls are elastic, what happens with the velocity of the ball after collision with a moving wall?

 

[Josh0768]

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]

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?