What Happens When a Ball Hits a Moving Wall?

[Domnu]

Problem
If you throw a ball with velocity $$v$$ at a wall, it rebounds with the same speed, $$v$$. What happens if you throw it at speed $$v$$ towards a wall which is traveling towards you at speed $$w$$? What is your answer in the limit in which $$w$$ is much larger than $$v$$?

Answer
Let us work in the frame of the wall. The ball comes towards you at velocity $$v+w$$, so it must leave at velocity $$v+w$$ with respect to you. Moving back to the lab frame, this means that the ball moves now, to the left with velocity $$v+2w$$. In the limit where $$w$$ is much larger than $$v$$, the velocity of the ball is $$2w$$.

Is my answer correct?

 

[Doc Al]

Looks good to me!