# Thread: The maximum height of a bouncing ball.

1. ## The maximum height of a bouncing ball.

My question is about b) which is asking for the maximum height. Attached as well is the solutions manual:

It did take me a while to understand a) but I see that as h goes to zero that b-32t is left so for now I have to accept it and move on.

As for b) the solutions manual says that v(t) = 0 and that velocity is t =b/32.

OK fine it must be the answer however at this point b is not known or is it? I tried graphing the equation b-32t however I am finding my graphing calculator only allows for one variable or maybe I just havn't figured out how to work another variable b in.

The solutions manual goes on to describe s(b/32) = b^2/64 which also I am working on understanding but I just don't see how that was arrived at either.

Perhaps I could get some explanation?

P.S. I think both terms were multiplied by 1/32 and then solved for t to get b/32?

2. ## Re: The maximum height of a bouncing ball.

Actually it looks more like the b/32 is the derivative solved for t. I could use some verification that is correct. It looks like this thing about b is all conceptual and is meant to apply to an equation with a real integer in place for b. I'm not sure about any of this yet.

Hopefully I have the terminology correct when I refer to the derivative.

3. ## Re: The maximum height of a bouncing ball.

The solution manual is correct.

Originally Posted by sepoto
OK fine it must be the answer however at this point b is not known or is it?
Throughout this problem, b is a parameter, meaning that all quantities have to be expressed through b.

Originally Posted by sepoto
I tried graphing the equation b-32t however I am finding my graphing calculator only allows for one variable or maybe I just havn't figured out how to work another variable b in.
You need to provide a concrete value of b; then you can graph it as a function of t.

Originally Posted by sepoto
The solutions manual goes on to describe s(b/32) = b^2/64 which also I am working on understanding but I just don't see how that was arrived at either.
s(b/32) = b(b/32) - 16(b/32)^2 = b²/32 - 16b²/(32)² = b²/32 - b²/(2*32) = b²/32 - b²/64 = b²/64.