Question

A ball is dropped from a height h above the
landing and bounces down a flight of stairs as
shown in figure. Determine the value of h for
which the ball will bounce the same height
above each stop. Coefficient of restitution
between stairs and ball is e.
h
h
d
h
d​

Answer 1

For a stair step, ball free falls from h height, so velocity when it touches the step is

2gh

So the velocity of rebound is e

2gh

The height it reaches is e

2

×2gh/2g=e

2

h

As e

2

h+d=h, where d is the height of step.

So,

d

h

=

1−e

2

1