A ball is projected vertically down with an initial velocity from a height of $ 20 m$ onto a horizontal floor. During the impact it loses $ 50\% $ of its energy and rebounds to the same height. The initial velocity of its projection is ............ $\mathrm{m} / \mathrm{s}^{-1}$
A ball is projected vertically down with an initial velocity from a height of $ 20 m$ onto a horizontal floor. During the impact it loses $ 50\% $ of its energy and rebounds to the same height. The initial velocity of its projection is ............ $\mathrm{m} / \mathrm{s}^{-1}$
$20$
$15$
$10$
$5$
A ball is projected vertically down with an initial velocity from a height of $ 20 m$ onto a horizontal floor. During the impact it loses $ 50\% $ of its energy and rebounds to the same height. The initial velocity of its projection is ............ $\mathrm{m} / \mathrm{s}^{-1}$
Let ball is projected vertically downward with velocity $v$ from height $h$
Total energy at point $A = \frac{1}{2}m{v^2} + mgh$
During collision loss of energy is $ 50\%$ and the ball rises up to same height. It means it possess only potential energy at same level.
$50 \%$ $\left( {\frac{1}{2}m{v^2} + mgh} \right) = mgh$
$\frac{1}{2}\left( {\frac{1}{2}m{v^2} + mgh} \right) = mgh$
$v = \sqrt {2gh} = \sqrt {2 \times 10 \times 20} $
$v = 20\,m/s$
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