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5.Work, Energy, Power and Collision
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A particle of mass $m$ strikes the ground inelastically, with coefficient of restitution $e$
A
$\frac{{\tan \,\alpha }}{{\tan \,\theta }} = e$
B
$\frac{{\tan \,\theta }}{{\tan \,\alpha }} = e$
C
${\tan ^2}\,\theta + {\tan ^2}\,\alpha = 1$
D
${\tan ^2}\,\theta + {\tan ^2}\,\alpha = {e^2}$
Solution
$\mathrm{v} \cos \alpha=\mathrm{e} \mathrm{u} \cos \theta$ $…(1)$
and $v \sin \alpha=u \sin \theta$ $…(2)$
$\mathrm{Eq}.(\text { ii }) / \mathrm{Eq}.(i)$
$\frac{v \sin \alpha}{v \cos \alpha}=\frac{u \sin \theta}{\operatorname{eu\,cos} \theta}$
$\tan \alpha=\frac{\tan \theta}{\mathrm{e}} \rightarrow \frac{\tan \theta}{\tan \alpha}=\mathrm{e}$
Standard 11
Physics
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