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## Homework Statement

A person drops an object of mass m from a height H. Show that the miss distance must be at least

[tex]\Delta x = (\frac{\hbar}{m})^{1/2}(\frac{H}{2g})^{1/4}[/tex]

## Homework Equations

[tex]\Delta p_x\Delta x \ge \frac{\hbar}{2}[/tex]

## The Attempt at a Solution

I'm at a total loss. Where is the source of uncertainty in momentum here? There doesn't seem to be any. If there were, it would have to be uncertainty in the momentum in the x direction which is what? Height, perpendicular to the floor? Or some unspecified but arbitrary direction parallel to the floor? There seems to be some clue in the fact that the uncertainty principle equation is linear in hbar, but the uncertainty in the problem is proportional to the square root of hbar. One more thing I don't understand is that the uncertainty principle guarantees uncertainty in measurements, not inaccuracy. What guarantees a minimum miss distance?