# Ball rebounding to less than initial height

1. Oct 30, 2004

### MattF

Hi, I have a homework problem that's giving me a bit of trouble. I hope someone can help me out and verify whether I'm correct or not :)

After falling from rest at a height of 30 meters, a 0.50 kilogram ball rebounds upward, reaching a height of 20 meters. If the contact between ball and ground lasted 0.002 seconds, what average force was exerted on the ball?

Ok, here is how I went about solving this. Using free-fall equation final velocity squared = initial velocity squared + (2 * gravity * height) (g=9.81), I determined that the ball impacted the ground at 24.261 m/s.

Then, using the same equation I determined that to reach a height of 20 meters it had to leave the ground at an initial velocity 19.81 m/s.

Thus, for average force:

F=ma=(mass*change in velocity)/time=[0.5 kg*(19.81 m/s - (-24.261 m/s)]/0.002 seconds

Force= 11020 Newtons

Phew, am I correct?

2. Oct 30, 2004

### arildno

Welcome to PF!
Looks good to me..

3. Oct 30, 2004

### Clausius2

Wow, I think you have a new medal:

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====CONGRATULATIONS===
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I've tried to make a Norwegian banner, but it's a bit difficult .

4. Oct 30, 2004

### arildno

Thank you..:shy:
I'll start canvassing for your next one in return..