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**Problem**

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

**Answer**

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

Is my answer correct?