Gas molecule and moving wall collision

[ian2012]

Homework Statement

Gas is contained in an enclosure in which one of the walls is a plane of area A. The wall
acts as a frictionless piston, moving with constant velocity u in the positive x-direction,
thus increasing the volume V of gas enclosed.

A gas molecule of mass m approaches the moving wall at velocity v = (vx, 0, 0),
relative to the enclosure. Obtain an expression for the velocity of the molecule after
it rebounds elastically from the moving wall.

Homework Equations

The Attempt at a Solution

So in the rest frame of the wall you have v = u - vx, and the rebounded velocity is just the negative of this. But how do you transform back to the lab frame? Or was it unnecessary transforming into the rest frame of the wall in the first place? I am confused?

 

[nickjer]

Remember, the molecule is traveling faster than the wall, so you might want it set as v = vx -u. Also, once you solve it you will definitely need to go back to the lab frame.