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## Homework Statement

After falling from rest from a height of 30m, a .50 kg ball rebounds upward, reaching a height of 20m. If the contact between ball and ground lasted 2.0ms, what average force was exerted on the ball?

## The Attempt at a Solution

What I did was drew a nice little picture with the 30m and the 20m and the little 2ms interval between them.

So I tried to first figure out what the change in acceleration was while the ball was in contact with the ground.

So I found the velocity when the ball hits the ground using first [tex]\Delta[/tex]y=vot+ayt^[tex]^{2}[/tex] and I found that t=2.5 seconds. So then putting that into the equation v=vo+at I got that the v on impact =-24.5m/s.

So then I tried to find the velocity when the ball leaves the ground. So I know that it travels 20m upwards, at that at the top of the 20m v=0. So I plugged those two things into v[tex]^{2}[/tex]=vo[tex]^{2}[/tex] + 2a[tex]\Delta[/tex]x and I solved for vo. I found that vo was 19.79m/s.

So I think at this point I have that when the ball hits the ground, v=24.5m/s, and when the ball leaves the ground v=19.79m/s and that the ball is in contact with the ground for 2ms.

So I said that a=[tex]\Delta[/tex]v/[tex]\Delta[/tex]t and I got that a=-2355m/s[tex]^{2}[/tex].

So my force in those 2ms =ma =.50kg(-2355m/s2) = -1177.

So since it asks for the average force exerted on the ball I think I'm supposed to get some other forces and then average them together with that one. So I said at the top of the 30m F=0 (before the ball is dropped). The ball hits the ground with an acceleration of -9.8m/s[tex]^{2}[/tex] so the force on impact is (.5kg)(-9.8)=-4.9N. At the top of the 20m rebound a is also -9.8 so the force is the same, -4.9.

So at this point I'm feeling like I'm making this much more complicated that it needs to be, but I add all those forces together:

-4.9+-4.9+0+-1177 and divide by 4 = -296N.

Unfortunately this is the wrong answer, so says the answer key and I can't figure out what to do.

Help?

Hopefully trolling through all of my attempts won't be too daunting.

Thanks!