A person is standing at the top of a 58.0m tall hill. He stumbles and falls.As he rolls down the hill, magically friction has no effect on him! When he is still 25.0m above the base of the hill determine how fast he is moving.

Answer 1

If friction has no effect, why would he roll and not just slide?

I will assume in fact that there is no friction and he does not roll so translational kinetic energy is all the kinetic energy he has (no rotational)
58-
change in potential energy = m g (25 -58)
change in kinetic energy = (1/2) m v^2
so
m v^2 / 2 - 33 m g = 0 = change in total energy
so
v = sqrt (66 g)
= sqrt (66*9.81)
= 25.4 m/s

Answer 2

V^2 = Vo^2 + 2g*d
V^2 = 0 + 19.6*(58-25) = 646.8
V = 25.43 m/s.