Physics - Heisenberg Uncertainty Principle - Marble Drop (Q 1)

Scenario: You are going to drop a marble with mass m from the top of a building of height H onto a small target below it.

1) Obtain an expression for the time it takes for the marble to fall height H.  Assume marble is dropped from rest.

2) According to uncertainty principle, marbles don't necesarily fall straight down from the release point to the center of the target, but are affected by the initial conditions.  If the location of the release point is uncertain by an amount  perpendicular to the vertical direction, write an expression for the resulting minimum uncertainty inthe horizontal component of the speed 

3) Write an expression for the resulting uncertainty in the horizontal displacement  of the marble when it reaches the ground.  Be sure to add the initial horizontal uncertainty of the release point.