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= x0 +v0t + 1/2 at2, 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 = v0 + 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/s2) (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)