In this problem you will investigate the feasibility of quantum uncertainty effects playing a role in a simplified version of pinball.
In this version of pinball, the table is flat so that gravity plays no role. There is a series of small pins of negligible radius at an average spacing of D=10 cm. The object is to hit a small ball (mass m=10 g, radius R=1 cm) at a velocity of v=10 cm/s at just the right angle and impact parameter so that it collides with a predetermined series of pins eventually entering the goal. (See Figure 1.) You will show in this problem that after a relatively small number of collisions with pins, even under ideal circumstances, it is impossible to have the ball enter goal on a regular basis. Such regular behavior would directly violate the Heisenberg Uncertainty Principle (HUP) of quantum mechanics.
