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A ball is projected vertically down with a velocity of $10 m s^{- 1}$ from a height of 10m. On hitting the ground if it loses 50 % of its energy, the height to which it bounces is $(g = 10 m s^{- 2})$

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10m

7.5m

answer is C.

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Detailed Solution

$\frac{50}{100} [\frac{1}{2} m \times 100 + m \times 10 \times 10] = m \times 10 \times h$

$\frac{1}{2} m [50 + 100] = m \times 10 h$

$\frac{1}{2} \times 150 = 10 h \Rightarrow 7.5 m$

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