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.

New contributor
Amal Antony is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – John Rennie, Aaron Stevens, GiorgioP, Qmechanic
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ If the ball collides elastically then it would keep on following the same motion for infinite time and infinite number of collisions. $\endgroup$ – harshit54 Mar 15 at 6:09
  • $\begingroup$ It was asked to find the number of collisions the ball has made with the ground,in the given time interval ,t=8s. $\endgroup$ – Amal Antony Mar 15 at 6:13
  • $\begingroup$ Can you show us the graph you plotted? $\endgroup$ – harshit54 Mar 15 at 6:14
  • $\begingroup$ 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. $\endgroup$ – Amal Antony Mar 15 at 6:21
  • 1
    $\begingroup$ @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 $s(=20\mbox{m})$ . $\endgroup$ – John Forkosh 2 days ago