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

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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 $g=10 \, m \, s^{- 2}$ )

NTA AbhyasNTA Abhyas 2020Work, Energy and Power

Solution:

Solution
kinetic energy of the ball on reaching ground
$K E_{1} = m g h + \frac{1}{2} m v_{0}^{2}$
after collision $\frac{K E_{1}}{2} = m g h$
$\frac{m g h + \frac{1}{2} m v_{0}^{2}}{2} = m g h$
$v_{0} = \sqrt{2 g h} = 20 \, \text{m} \, \, \text{s}^{- 1}$