A 47.5-g ball moves at 30.0 m/s. If its speed is measured to an accuracy of 0.20%, what is the minimum uncertainty in its position

The minimum uncertainty in its position is 1.85 x 10⁻³² m.

Explanation:

Given;

mass of the ball, m = 47.5 g = 0.0475 kg

speed of the ball, v = 30 m/s

measuring accuracy of the speed, = 0.2% = 0.002

The uncertainty in measurement of momentum;

ΔP = mΔv

ΔP = (0.0475)(30 x 0.002)

ΔP = 2.85 x 10⁻³ kgm/s

The uncertainty in position is calculated as;

where;

h is Planck's constant

Thus, the minimum uncertainty in its position is 1.85 x 10⁻³² m.