Uncertainty Principle Homework: Minimal Width of Crack

[asi123]

Homework Statement

Hey guys.

I have this kid throwing a ball with mass M and from high H.
He is trying to hit a crack in the floor.
I need to show that in order for the ball not to miss the crack, the minimal width of the crack (delta x) should be the expression in the red box in the pic.

http://img43.imageshack.us/img43/6563/scan0001fon.jpg

I wrote down about everything I know about the Uncertainty principle...
How can I find the connection between (delta v) and v?

Thanks.

Homework Equations

The Attempt at a Solution

 

[chiro]

The uncertainty principle states in brief that when you measure momentum and distance you relate the two in the form

delta_p * delta_x >= h/2 where h is Plancks constant and the deltas are the statistical deviations from the mean of the random variable.

If you want a good mechanism on explaining quantum mechanics you should read a book by Feynman and Hibbs called the Path Integral formulation written by a famous physicist called Richard Feynmann. It goes into great detail explaining the formulation of quantum mechanics using functionals.

I'm about to study it myself in great detail but I have seen a copy already and it is very very good.

Basically the derivation involves assuming a gaussian distributed random variable and then taking the various deviations on that variable. There is a better explanation of this in books involving descriptions of wave mechanics.

Anyway hope that helps.

 

[diazona]

Homework Statement

Hey guys.

I have this kid throwing a ball with mass M and from high H.
He is trying to hit a crack in the floor.
I need to show that in order for the ball not to miss the crack, the minimal width of the crack (delta x) should be the expression in the red box in the pic.

http://img43.imageshack.us/img43/6563/scan0001fon.jpg

I wrote down about everything I know about the Uncertainty principle...
How can I find the connection between (delta v) and v?

Thanks.

Kind of a weird problem... you'd think that in order for the ball not to miss the crack, the ball has to be smaller than the crack! I have a suspicion that this is not a proper application of the uncertainty principle. But I probably shouldn't say anything without knowing how to solve the problem, and right now I can't see any connection between the physical situation and the answer you're supposed to get.