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Q.

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v₀. It collides with the ground and loses 50% of its energy in collision and rebounds to the same height. The initial velocity v₀ is : (Take g = 10 ms^-2)

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a

10 ms^-1

b

14 ms^-1

c

28 ms^-1

d

20 ms^-1

answer is A.

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Detailed Solution

When ball collides with the ground it loses its 50% of energy

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$∴ \frac{{KE}_{f}}{{KE}_{i}} = \frac{1}{2} \Rightarrow \frac{\frac{1}{2} {mv}_{f}^{2}}{\frac{1}{2} {mv}_{i}^{2}} = \frac{1}{2}$

or $\frac{V_{f}}{V_{i}} = \frac{1}{\sqrt{2}}$

or, $\frac{\sqrt{2 gh}}{\sqrt{v_{o}^{2} + 2 gh}} = \frac{1}{\sqrt{2}}$

or, $4 gh = v_{o}^{2} + 2 gh$

$∴ v_{o} = 20 {ms}^{- 1}$

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A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground and loses 50% of its energy in collision and rebounds to the same height. The initial velocity v0 is : (Take g = 10 ms-2)