# Heisenberg Uncertainty Principle Question

1. Jul 31, 2009

### kongieieie

Sorry about not using symbols but I haven't learnt how to do that yet.

1. The problem statement, all variables and given/known data

A woman is on a ladder of height H. She drops small rocks of mass m toward a point target on the floor.

Show that according to the Heisenberg Uncertainty Principle, the average miss distance must be at least

delta(x final) = sqrt [h/pi*m] * sqrt sqrt [2H/g]

where h is the planck's constant,
pi is 3.14
m is the mass of the rock
H is the height from which the rock is dropped
g is the acceleration due to gravity.

Assume that delta(xfinal ) = delta(x initial) + (delta(v))*t
Also justify the assumption.

2. Relevant equations

delta(x) * delta(p) < or = [h/4*pi]

delta(p) = m * delta(v)

v= u +at
s= 0.5(u + v)t
s= ut +0.5at^2
v^2= u^2 +2as

3. The attempt at a solution

I did a couple of substitutions and got something like t=sqrt[2H/g] and delta(v)=sqrt[2gH] but I can't seem to get the equation needed. Tried for 2 hours and can't seem to understand it all. Please help? Or at least give some hints. Also, I don't know how to justify the assumption above.

2. Aug 26, 2009