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 one-dimensional 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 counter-forces (plus it gives a positive answer)