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Question

A ball after freely falling from a height of 4.9 m strikes a fixed horizontal plane. If the coefficient of restitution is 34, after what time interval the ball will strike the plane second time :

A
0.5 s
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B
1 s
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C
1.5 s
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D
2 s
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Solution

The correct option is C 1.5 s
According to question,

Velocity of ball just before striking plane, v
using,
v2u2=2as
v=2×9.8×4.9=9.8 m/s ...(1)
Since horizontal plane remains fixed, initial and final velocity of the plane remains same.
Rebound velocity, v=ev
=34×v [e=3/4, given]
=34×9.8 [from (1)]
=7.35 m/s..... (2)
Let us suppose, after t time ball again strikes the plane
As ball reaches to same position, its displacement is zero.
Using, s=ut+12at2
0=7.35t12×9.8×t2 [from (2), u=v]
t=7.35×29.8
t=32=1.5 s
After 1.5 s ball will strike the plane for the second time.

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