A ball is thrown up in the air with an initial speed of V. If the air exerts a constant frictional force F on the ball, show that H = (V^2) / 2(g+F/m)

Answer 1

Subtract the work done against friction (F*H) from the initial kinetic energy. That will equal the potential energy increase.

(1/2) m V^2 - F H = m g H
(1/2) m V^2 = H(mg + F)

One more step and you're there.