A rubber ball is dropped from a height of 5 m on a planet where the acceleration due to gravity is not known. On bouncing, it rises to 1.8 m. The ball loses its velocity on bouncing by a factor of
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If ball falls from height $h_{1}$ and bounces back up to height h_2 then $e = \sqrt{\frac{h_2}{h_1}}$
Similarly, if the velocity of ball before and after collision are $V_1$ and $V_2$ respectively then $e = \frac{V_2}{V_1}$
So $\frac{v_2}{v_1} = \sqrt{\frac{h_2}{h_1}} = \sqrt{\frac{1.8}{5}} = \sqrt{\frac{9}{25}} = \frac{3}{5}$
i.e. fractional loss in velocity $= 1 - \frac{v_2}{v_1} = 1 - \frac{3}{5} = \frac{2}{5}$
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