Uncertainty Principle: Missing Target by Typical Distance

[asdfghjkl]

Can anyone help me on this??

In a contest to drop a marble with mass 30 g from the roof of a building onto a small target 50 m below. From uncertainty principle considerations, what is the typical distance by which you will miss the target, given that you aim with the highest possible accuracy? Ignore wind and air resistance.

[Hint: Let x be the coordinate in the horizontal direction. You should realize that the uncertainty in the position x of the marble when it reaches the ground depends on both the initial uncertainty in the position xi, and the initial uncertainty in the speed vx.]

 

[quantumdude]

Let the initial position x₀ lie in the interval:
[-d_x,d_x]

Let the initial velocity v₀ lie in the interval:
[-d_v,d_v]

Now use the ordinary kinematic equations to figure out the extreme values of x(t) and v(t) when the marble hits the target.

 

[jackle]

Would the uncertainty principle apply to a marble?

I was always told that it applied to sub-atomic particles. Even atoms were supposed to obey semi-classical formula in my education.

 

[jackle]

I've had a longer think about this question (and I haven't done any active physics for years, please forgive the poorly articulated argument) but I would expect the following:

A particle of uncertainty dX has 2/3 chance of being in the region
x +/- dx.

Two particles each with an uncertainty of dx in a system (ignoring the interactions) should have a centre with a lower uncertainty. Even if both particles are outside the 2/3 probability, if one is on the extreme left and one on the extreme right, this would cancel.

So a mole of particles(or say 10^23) should have a centre with almost no uncertainty even without taking into account the structure of the substance.

I reason that the same is true of particle momenta.

I think this reasoning is wrong because you are all brilliant and I'm useless (and the marble question sounds like a formal one). But why?

Sorry this post was put together at lunch in a cafe. I usally have time to make a proper go of it.