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Question

A tennis ball is thrown from the height h above the ground. If the ball strikes to the ground with elastic collision,what height will height will the ball achieve after the first collision?


A
he6
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B
e2h
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C
e3h
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D
none of these
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Solution

The correct option is B $$ e^2h $$

Given,

Initial height = $$h$$

Coefficient of elasticity, $$e\equiv \dfrac{{{v}_{final}}}{{{v}_{inital}}}=\sqrt{\dfrac{{{K}_{final}}}{{{K}_{initial}}}}=\sqrt{\frac{{{K}_{1}}}{{{K}_{0}}}}$$

$$ {{K}_{1}}={{e}^{2}}{{K}_{0}} $$

$$ mgh_1={{e}^{2}}mgh $$

$$ {{h}_{1}}={{e}^{2}}h $$

Hence, height after first collision is $${{e}^{2}}{h}$$


Physics

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