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Q.

A ball is thrown vertically downwards from a height of 20 m with an initial velocity $V_{0}$ . It collides with the ground loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity $V_{0}$ is : (Take g = 10 ms^–2)

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a

$10 m s^{- 1}$

b

$20 m s^{- 1}$

c

$28 m s^{- 1}$

d

$14 m s^{- 1}$

answer is A.

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Detailed Solution

$∴ \frac{K E_{f}}{K E_{i}} = \frac{1}{2} \Rightarrow \frac{\frac{1}{2} m V_{f}^{2}}{\frac{1}{2} m V_{i}^{2}} = \frac{1}{2} o r \frac{V_{f}}{V_{i}} = \frac{1}{\sqrt{2}}$
or $\frac{\sqrt{2 gh}}{\sqrt{V_{0}^{2} + 2 gh}} = \frac{1}{\sqrt{2}} or 4 gh = V_{0}^{2} + 2 gh$
$∴ V_{0} = 20 m s^{- 1}$

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