Question

A ball is let to fall form a height It makes ‘n’ collisions with the horizontal ground. If after ‘n’ collisions it rebounds with a velocity and the ball rises to a height h, then the coefficient of restitution for the collision is

Answer 1

Answer:

Height = h

0

collision is = v

n

height = h

n

coefficient of restitution = e

The velocity of the earth before and after collision may be assumed zero.

Hence e

n

=

v

0

v

1

×

v

1

v

2

×

v

2

v

3

×.........

v

n−1

v

n

v

n

= velocity after n

th

rebound

v

0

= velocity with which the ball strikes the earth first time

Hence e

n

=

v

0

v

n

=

2gh

0

2gh

n

e

n

=

h

0

h

n