Solving Planck's Uncertainty Problem for Baseball Motion

[georgeh]

Imagine playing baseball in a universe where Planck's constant was 0.60 J-s. What would be the uncertainty in the position of a .50 kg baseball that is moving 20 m/s with an uncertainty of 1.0 m/s?
so i know, delta X*delta P=(plancks constant/2pi)/2
I solve for x. and it will tell me the uncertainty for position in the x,
my question is, how do i find out the percent uncertainity for this problem?
Do i do, 1/20 and that will give me % uncertainty? i know basic question..but any help is appreciated.

 

[big man]

You almost have it. When you divide the uncertainty by the actual value it is called the relative uncertainty. So 1/20 will give you the relative uncertainty and it isn't the percentage uncertainty. The percentage uncertainty is simply found by multiplying the relative uncertainty by 100.

ie $$\\frac{\Deltax}{x}(100)=% uncertainty$$

Edit: I still don't see the above latex properly so I will just put it in text here.

% unc = [delta(x)/x]*100

So obviously once you find the momentum ($$p=mv$$), multiply by the RELATIVE uncertainty (will be 1/20 in your case) to find the uncertainty in momentum. You then solve for x like you said, but remember this will give you the absolute uncertainty in the position...so unless you know the inital value for x you can't find the percentage uncertainty for the position.

That last paragraph was probably not necessary, but I thought it might explain a bit more ??