Question asked by Filo student

A small ball is dropped from rest from height $10\mathrm{m}$ on a horizontal floor. If coefficient of restitution between ground and body is $0.5$, then find the maximum height it can rise after collision. The ball is dropped from height $h_1$, so velocity just before hitting the ground = velocity of approach $=V_{\text{approach }}=\sqrt{2g{h}_1}$ The ball rises to the height $h_2$, so velocity when just leaves the ground = velocity of separation $=\sqrt{2g{h}_2}=V_{\text{separation }}$ Coefficient of restitution, $\begin{array}{rl}e& =\frac{V_{\text{separation }}}{V_{\text{approach }}}\\ \Rightarrow e& =\sqrt{\frac{2g{h}_2}{2g{h}_1}}=\sqrt{\frac{h_2}{h_1}}\\ \Rightarrow h_2& =e^2{h}_1=\frac{1}{4}\times 10=2.5\mathrm{m}\end{array}$

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Updated on: Nov 8, 2022