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teme92

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## Homework Statement

A dart of mass ##m## is dropped from a height ##l##. Formulate the uncertainty principle and estimate the minimum limitations, set by the uncertainty principle, of the accuracy that can be achieved in the lateral ##x## position after falling, given an original uncertainty ##\Delta x##, and no original uncertainty in y.

## Homework Equations

## The Attempt at a Solution

The time to drop is ##\sqrt{2l/g}##. With uncertainty the dart hits the ground at a distance ##R## where:

##R=\Delta x+\sqrt{2l/g}\space \Delta p/m \geq\Delta x +\sqrt{2l/g}\space \hbar/2m\Delta x##

This next part I found from a book but I don't understand how its got from above:

##\Delta x=(l\hbar^2/2m^2g)^{\frac{1}{4}}##

with ##R\geq(8l\hbar^2/m^2g)^{\frac{1}{4}}##

Could anyone clarify how ##\Delta x## and ##R## were found?

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