A ball is thrown vertically downwards from a height of $20 \mathrm{~m}$ with an initial velocity $\mathrm{V}_{0}$. 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 $g=10 \mathrm{~ms}^{-2}$ ) (1) $10 \mathrm{~ms}^{-1}$ (2) $14 \mathrm{~ms}^{-1}$ (3) $20 \mathrm{~ms}^{-1}$ (4) $28 \mathrm{~ms}^{-1}$

Home » A ball is thrown vertically downwards from a height of with an initial velocity . It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity is: (Take ) (1) (2) (3) (4)

A ball is thrown vertically downwards from a height of $20 \mathrm{~m}$ with an initial velocity $\mathrm{V}_{0}$ . 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 $g=10 \mathrm{~ms}^{-2}$ ) (1) $10 \mathrm{~ms}^{-1}$ (2) $14 \mathrm{~ms}^{-1}$ (3) $20 \mathrm{~ms}^{-1}$ (4) $28 \mathrm{~ms}^{-1}$

Physics | Physics

A ball is thrown vertically downwards from a height of $20 \mathrm{~m}$ with an initial velocity $\mathrm{V}_{0}$ . 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 $g=10 \mathrm{~ms}^{-2}$ ) (1) $10 \mathrm{~ms}^{-1}$ (2) $14 \mathrm{~ms}^{-1}$ (3) $20 \mathrm{~ms}^{-1}$ (4) $28 \mathrm{~ms}^{-1}$

Solution: (3)

$\begin{array}{l} \frac{K E_{f}}{\mathbb{K E}_{i}}=\frac{1}{2} \\ \frac{V_{f}}{V_{i}}=\frac{1}{\sqrt{2}} \\ \frac{\sqrt{2 g h}}{\sqrt{V_{0}^{2}+2 g h}}=\frac{1}{\sqrt{2}} \end{array}$