Consider the motion of the ball in its lowest allowed Bohr-Sommerfeld
orbit. Based on the picture of experiments carried out on balls at
random points in such an orbit, give estimates for both
the expected spread in the distribution of measured heights, 
, and the spread in the distribution of measured momenta,
. In both cases express your results only terms of the
parameters m, g and h. Then, show that the ground
state is at approximately the limit which the Heisenberg Uncertainty
Principle (HUP) imposes.