Suppose you drop a ball-bearing a vertical distance y=2.2m onto a bulls-eye on the floor.?

Question

According the Heisenberg's uncertainty principle, the BBs do not fall straight down from the release point to the center of the bullseye, but are affected by the initial conditions. a)if the location point is uncertain by an amount ^x=0.1mm in the horiz. direction, calculate the miniumum spread ^X of the impacts. b) If there is an uncertainty ^y=0.1mm in the release point, what is ^X? c)Would this affect your darts game accuracy?

Answer 1

(a) the initial deflection will be projected directly down onto the 'bull's eye'. So .1mm deflection will result in a .1mm radius about the perfect projection.
If we introduce horizontal velocity as a part of initial condition then the uncertainty radius will increase proportionately to the initial horizontal velocity and height the ball has to fall.
The height will determine the time the ball remains in the air. The ball will use that time to move horizontally due to its horizontal velocity component.
(b) The change in release point vertically will not influence the distribution unless coupled with variations in horizontal release.
(c) Yes it will based on reasoning discussed above.

(Interesting question)

Answer 2

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