A ball is dropped from a height h. If the coe | vedclass

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(D) When a ball is dropped from a height $h$,the velocity just before the first impact is $v_0 = \sqrt{2gh}$.After the first collision with the ground

Vedclass · Accepted Answer

$e^4h$

Vedclass · Answer

(D) When a ball is dropped from a height $h$,the velocity just before the first impact is $v_0 = \sqrt{2gh}$.After the first collision with the ground,the velocity becomes $v_1 = ev_0 = e\sqrt{2gh}$.The height reached after the first collision is $h_1 = \frac{v_1^2}{2g} = \frac{e^2(2gh)}{2g} = e^2h$.After the second collision,the velocity becomes $v_2 = ev_1 = e^2\sqrt{2gh}$.The height reached after the second collision is $h_2 = \frac{v_2^2}{2g} = \frac{e^4(2gh)}{2g} = e^4h$.In general,the height reached after $n$ collisions is given by $h_n = h e^{2n}$.For $n = 2$,the height is $h_2 = h e^{2(2)} = e^4h$.

$A$ ball is dropped from a height $h$. If the coefficient of restitution is $e$,to what height will it rise after jumping twice from the ground?

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