## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

The potential energy at the maximum height is equal to the kinetic energy at the initial position. $PE_1 = KE_0$ $mgh = KE_0$ $h = \frac{KE_0}{mg}$ Let's suppose that the kinetic energy is $2KE_0$ at the initial position and let $h_2$ be the height the ball reaches. $PE_2 = 2KE_0$ $mg~h_2 = 2KE_0$ $h_2 = \frac{2KE_0}{mg}$ $h_2 = 2~\frac{KE_0}{mg}$ $h_2 = 2~h$ The ball will thus reach a height of 2h.