A ball is thrown straight up into the air with a speed of 13 m/s. If the ball has a mass of 0.25 kg, how high does the ball go? Acceleration due to gravity is g = 9.8 m/s2
A. 9.2 m
B. 8.6 m
C. 10.4 m
D. 9.9 m

The total energy, i.e. sum of kinetic and potential energy, is constant.

i.e. E = KE + PE

Initially, PE = 0 and KE = 1/2 mv^2

At maximum height, velocity=0, thus, KE = 0 and PE = mgh

Since, total energy is constant (KE converts to PE when the ball is rising),

therefore, KE = PE 

or, 1/2 mv^2 = mgh

or, h = v^2 /2g = 13^2 / (2x9.8) = 8.622 m

Hope this helps.