To determine height of the block, first we need to determine the average force exerted by the ball to the block.

Because it has been told that , we can ignore the velocity changes due to gravity.

When the ball collides with the block, the block give the change of momentum of the ball with value of

And the average time taken by the ball to collide with the block once is

Consider the ball has bounced with the block for N times (N>>1). Then the total change of ball's momentum caused by the block only is,

And the total time to bounce N times with the block is,

Then the average force exerted to the block is,

The force have to cancel the weight of the block,

Therefore,

The solution is very simple, but it's hard to get there. :)

That's my solution.

If you have any question, correction, or comments, please leave a comment below.

Thank you.

## 2 comments

this question is really good ...i got it in first attempt.feeling really good :)

I have to admit that it's a great point to add N to delta(Ptot) and delta(Ttot). If we don't put N in, we still have the same result, but that will be a nearly wrong solution!

However you forgot to state the assumption that the collision is totally elastic.

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