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From a point on smooth floor of a room a toy ball is shot to hit a wall. The ball then returns back to the point of projection. If the time taken by ball in returning is twice the time taken in reaching the wall, find the coefficient of restitution.

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$e = 0.2$

$e = \frac{1}{2}$

$e = \frac{1}{3}$

$e = \frac{1}{4}$

answer is A.

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Detailed Solution

Horizontal disp. from projection to wall

$v_{1} t_{1} = v_{2} t_{2} |t_{2} = 2 t_{1}| \frac{v_{2}}{v_{1}} = \frac{1}{2} = e$

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