# Find number of collisions [on hold]

A ball dropped from a certain height,falls in the influence of uniform gravity,strikes the ground and rebounds elastically.During a time interval t=8s from it was dropped,it covers a distance s=20m.How many collisions n during this time did the ball made with the ground?Acceleration of free fall=10 m/s^2.

I found this problem in one of my textbooks.I tried to solve it, by plotting a speed vs time graph for the motion,and use the fact that the area under this graph gives the distance covered by body.

But I think the given information is insufficient,or is there any alternate way of solving this problem which connects the given variables to find n.

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## put on hold as off-topic by John Rennie, Aaron Stevens, GiorgioP, Qmechanic♦Mar 15 at 10:20

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• If the ball collides elastically then it would keep on following the same motion for infinite time and infinite number of collisions. – harshit54 Mar 15 at 6:09
• It was asked to find the number of collisions the ball has made with the ground,in the given time interval ,t=8s. – Amal Antony Mar 15 at 6:13
• Can you show us the graph you plotted? – harshit54 Mar 15 at 6:14
• It would be a triangular shaped periodic graph with speed increase to a peak(when it collides with ground) and then it starts to decrease uniformly to zero(when the ball reaches maximum height after bouncing).As this motion repeats,a perodic triangular graph is obtained. – Amal Antony Mar 15 at 6:21
• @AaronStevens Oops, right, that's a little trickier than I'd thought through, due to the sawtooth-like form for $v(t)$, with "inflection" every $t_0=\sqrt{2h/g}\,\mbox{secs}$. So you have to integrate that sawtooth "curve" from $0$ to $t(=8\mbox{secs})$ to get total distance travelled, and then find $h$ by demanding the integral evaluates to $s(=20\mbox{m})$ . – John Forkosh 2 days ago