P.E. is energy due to position
An easy kinematic equation can be used, and by taking it's 1st derivative and setting it = to 0, we can find the max height the ball is subjected to, and we can calculate that P.E.
1st eq; x= x_{0} +v_{0}t + 1/2 at^{2}, a simple kinematic eq for distance. Next take the1st derivative in terms of t, and set =0.
We basically have a onedimensional parabola we're finding the height of.
2nd eq (1st deriv.)  with some clean up > v = v_{0} + at. Next we are given an initial velocity, so solve for t and remember to set this 1st derivative =0 > 0=20 m/s + (9.8m *t) clean up & t=2.04 seconds
Going back to eq #1 and remembering that at the top of the parabola the ball is still > v=0
x= 0 + 0 + 1/2 (9.8m/s^{2}) (2.04 s)^{2}, we get x = 20.4 m.
*I chose +g in the last eq. because we were at a stop and there were no counterforces (plus it gives a positive answer)
6/28/2013

David R.