A basketball (which can be closely modeled as a hollow spherical shell) rolls down a mountainside into a valley and then up the opposite side, starting from rest at a height H0 above the bottom. In the figure, the rough part of the terrain prevents slipping while the smooth part has no friction.
a) How high, in terms of H0, will it go up the other side?
b) Why doesn't the ball return to height H0? Has it lost any of its original potential energy?