In this problem you will investigate the feasibility of quantum uncertainty effects playing a role in a simplified version of Pin Ball.
In this version of Pin Ball, the table is flat so that gravity plays no
role, and there is a series of small pins (of radius 
) at an
average spacing of D=10cm. The object is to hit a small ball (mass
m=10 g, radius small enough to ignore) at a horizontal velocity
(
) horizontally (along 
) at just the right angle and
height y so that it collides with a predetermined series of pins and
eventually enters the goal. (See figure below.) You will show that
after a relatively small number of pins, even under idea
circumstances, it is impossible to do this on a regular basis. Such
regular behavior is forbidden by the Heisenberg Uncertainty Principle
(HUP) of quantum mechanics.
