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**Homework Statement**

i) Find the average force exerted on a rubber ball mass m hitting a wall at speed v. The ball spends a time t in contact with the wall before bouncing off at speed v.

ii) The change in KE of the ball from when it hits the wall to when it is instantaneously at rest

iii) Assuming a steady force is acting on the ball, estimate the amount by which the ball is compressed during the collision

**The attempt at a solution**

i) This is easy enough

Average force = change in momentum / time taken = 2mv/t

ii) Again, easy: 0.5mv²

iii) If we assume the ball obey's Hooke's law (very rough, I know)

F=kx

=>2mv/t=kx or equivalently 2mvx/t=kx²

If all the KE of the ball is converted to EPE internally: mv²=kx²

Sub in kx²=2mvx/t giving 2mvx/t=mv²

Cancel and rearrange for x, the compression, giving: x=vt/2

The answers give vt/4, is there something I'm doing wrong? I'm guessing they made similar assumptions to me to get a similar answer but I can't see what I've done wrong.

Cheers.