# Coefficient of restitution of a ball bouncing down steps

1. Mar 12, 2013

### Daniel1992

1. The problem statement, all variables and given/known data

A small ball is placed at the edge of the top step of a flight of steps. Each step has identical
dimensions. The ball is kicked horizontally, perpendicular to the edge of the top step. On its first and second bounces it lands exactly in the middle of the first and second steps down from the top. Find the coefficient of restitution between the ball and the first step.

The ball continues bouncing down the steps hitting the middle of each successive step. What is the coefficient of restitution between the ball and the remaining steps?

I have been given the above problem to work. I am not sure where to start. All I know is that the coefficient of restitution is the ratio of speeds before and after the impact. Can anyone point me in the right direction?

2. Mar 12, 2013

### Staff: Mentor

The following questions should give a good start. Try to use them one by one, and see if you can continue yourself at some point.

Did you draw a sketch? This should include labels for some relevant parameters, like the step height and length.

How does the motion of the ball after the initial kick look like? In particular, how long does that last?

What do you know about the horizontal velocity component? How is that related to the motion after the first bounce? How is that related to the vertical component?