Question

A 220lb fullback runs the 40-yd dash at a speed of 19.6 ± 0.1 mi/h, what is the uncertainty in this position?

Answer 1

I found: `Deltax>=1xx10^-35m` (check my maths anyway). The mass and velocity involved are far too big to have a decisive impact to the uncertainty in a Quantum Mechanical sense.

Explanation:

Well, if you use Heisenberg's Uncertainty Principle (say, along the `x` direction) you need:
`Deltax` the uncertainty in position:
this is related to the uncertainty in momentum, `Deltap`, and Planck's Constant, `h`, through:
`color(red)(DeltaxDeltap>=h/(4pi))`
with your data (I changed to metric) and considering a constant mass (due to the low velocity involved) we get:
velocity`=19.6+-0.1 "mi/hr"=8.76+-0.04m/s`
mass`=220lb=99.79kg`
Plank's Constant`=6.63xx10^-34Js`

`Deltap=mDeltav=99.79*0.04=4kgm/s`

so that:
`Deltax>=(6.63xx10^-34)/(4*4*3.14)~~1xx10^-35m`
which is far smaller than any possible measurable distance (even using interferometric techniques, I think)!

The idea here, I think, is to "see" your body (the fullback) and measure his position. Something big as a person can be measured, basically, without interfering with it. On the other hand if you had a very small thing such as an electron, to "measure" it, you should "see" it using radiation that would interact with it changing its position or velocity introducing an uncertainty! So to measure something small changes its velocity/position.

It is like to throw sledgehammers to your running fullback to see where he is!!! You'll certainly "interfere" with his position/velocity!!!