You have entered a contest in which the contestants drop a marble with mass 27.0g from the roof of a building onto a small target 23.0m below.From uncertainty considerations, what is the typical distance by which you will miss the target, given that you aim with the highest possible precision?

Answer 1

If you use the Heisenberg uncertainty principle, the minimum error will be something like
sqrt[(h*R/(2 pi))/p]
where p is the nominal momentum at impact and R is the distance it falls.

You must be careful to recognized that the lateral position error depends upon the lateral momentum uncertaintly. You need to relate both to the angular deviation from a vertical fall.

It is more likely that the minimum position error will be governed by random turbulent eddy production in the wake of the marble, which has nothing to do with quantum mechanics. This goes beyond the scope of your physics question.