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The 'e' Equation

A ball falls ...

Question

A ball falls from a height of $5 m$ and strikes the roof of a lift. If at time of collision, lift is moving in the upward direction with a velocity of $1 m s^{- 1}$ . Then the velocity with which the ball rebounds after collision will be :

13 m s^{- 1}

upwards

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12 m s^{- 1}

downwards

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12 m s^{- 1}

upwards

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11 m s^{- 1}

downwards

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Solution

The correct option is C $12 m s^{- 1}$ upwards
Velocity of ball before collision $= \sqrt{2 g h} = \sqrt{2 \times 10 \times 5} = \sqrt{100} = 10 m / s$
Velocity of approach $= 10 - (- 1) = 11 m / s$
Velocity of separation $= (v - 1) m / s$
Since collision is elastic, e=1.
$11 = v - 1 v = 12 m / s$

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