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
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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
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