A ball moving with speed v normally towards a moving wall approaching it with speed u. The final speed of ball is (the collision is perfectly elastic)

The collision between the ball and the wall is perfectly elastic. In a perfectly elastic collision, the relative speed of approach is equal to the relative speed of separation.

Let's denote:

• Initial speed of the ball = v
• Speed of the wall = u
• Final speed of the ball = v'

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. However, since the wall is moving, we need to consider the frame of reference of the wall. In the wall's frame of reference, the initial speed of the ball is (v+u) and after the collision, the speed of the ball is (v'-u).

Since the collision is perfectly elastic, the relative speed of approach is equal to the relative speed of separation. Therefore, we have:

(v + u) = (v' - u)

Solving this equation for v', we get:

v' = v + 2u

So, the final speed of the ball, in the frame of reference of the wall, is v + 2u.