Right before bouncing, KE is ##\frac{1}{2}mv_{before}^2## and right after the bounce it is ##\frac{1}{2}e^2mv_{before}^2##, thus the fraction of KE lost each bounce should be ##1-e^2##, correct?
I know that the height before the first bounce will be ##y = g * t * t + v_0 * t + y_0##.
After the first bounce, I can find y by pretending the ball was thrown from the ground with velocity ##e * -v_f## with ##v_f## being the velocity of the ball when hitting the ground, but I have to reset the...