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An elevator platform is going up at a speed $20 m s^{- 1}$ and during its upward motion a small ball of 50 g mass falling in downward direction strikes the platform elastically at a speed $5 m s^{- 1}$ . Find the speed $(i n m s^{- 1})$ with which the ball rebounds.

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answer is 45.

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Detailed Solution

The situation is analysed in the figure we consider mass of platform to be very large compared to the of ball, so we have

${\vec{v}}_{1} = {\vec{u}}_{1} e = (\frac{v_{2} - v_{1}}{u_{2} - u_{1}}) = (\frac{v_{2} - u_{1}}{u_{1} - (u_{2})})$

${\vec{v}}_{2} = 2 {\vec{u}}_{1} = {\vec{u}}_{2}$

Thus rebound velocity of ball is

${\vec{v}}_{2} = 2 \times 20 - (- 5) = 45 m s^{- 1}$ upward.

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