A ball is dropped from a height of 5,m. The t | vedclass

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(C) The time taken for the first fall is $t_0 = \sqrt{\frac{2h}{g}}$.For $h = 5\,m$ and $g = 10\,m/s^2$,$t_0 = \sqrt{\frac{2 	imes 5}{10}} = 1\,s$.Th

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$3$

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(C) The time taken for the first fall is $t_0 = \sqrt{\frac{2h}{g}}$.For $h = 5\,m$ and $g = 10\,m/s^2$,$t_0 = \sqrt{\frac{2 	imes 5}{10}} = 1\,s$.The time taken for subsequent rebounds is given by $t_n = 2e^n t_0$.The total time $T$ is $t_0 + 2e t_0 + 2e^2 t_0 + \dots = t_0 [1 + 2(e + e^2 + e^3 + \dots)]$.Using the sum of an infinite geometric series $S = \frac{a}{1-r}$,where $a = e$ and $r = e$,we get $T = t_0 [1 + 2(\frac{e}{1-e})]$.Substituting $t_0 = 1\,s$ and $e = 1/2$:$T = 1 	imes [1 + 2(\frac{1/2}{1 - 1/2})] = 1 	imes [1 + 2(1)] = 3\,s$.

$A$ ball is dropped from a height of $5\,m$. The time after which the ball stops rebounding,if the coefficient of restitution between the ball and the ground is $e = 1/2$,is ............. $s$.

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