Physics - How does maximum height reached compare

We are studying momentum, work, potential, and kinetic energy. So although this may be solved in several ways please relate it back to those topics.

Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice that of Bill's. How does the maximum height reached by Joe's ball compare to the maximum height reached by Bill's ball?

Use conservation of energy:

For Bill 1/2 mv^2 = mgh ---> h = v^2/(2g)

Now let v --> 2v, then h --> h' = 2v^2/g

So Joe's ball travels 4 times hihger

Use conservation of energy:

For Bill 1/2 mv^2 = mgh ---> h = v^2/(2g)

Now let v --> 2v, then h --> h' = 2v^2/g

So Joe's ball travels 4 times hihger
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