Question

Consider a 2150-lb automobile clocked by law-enforcement radar at a speed of 85.5 mph (miles/hour). If the position of the car is known to within 5.0 feet at the time of the measurement, what is the uncertainty in the velocity of the car?

Answer 1

use the Schrodinger Equation~be careful with your units
(delta X)(delta P) > or = h/4pi

Mass(automobile)= 2150 lbs
1lbs=0.453592kg so:
2150lbs= 975.2236 kg

Uncertainty(delta X)= 5ft
1ft= 0.3048m so:
5ft= 1.524m

h= Planck's constant = 6.62606957 × 10-34 m2 kg / s

(delta V) = (delta P)/ Mass

Solving the original equation we get:

(delta V) = h/( (4pi)(Mass)(delta X) )
= (6.626X10^-34)/( (4pi)(975.2236kg)(1.524m)
=3.548x10^-38 m/s

I'm assuming we want our answer in mi/hr~

1m/s = 2.23694 mi/ hr so:
3.548x10^-38 m/s = 7.936x10^-38 mi/ hr