Consider a golf ball with a mass of 45.9 grams traveling at 200 km/hr. if an experiment is designed to measure the position of the golf ball at some instant of time with a precision of 1 mm, then what will be the uncertainty in the speed of the golf ball? what percentage of the speed of the golf ball does this uncertainty represent?

speed of golf ball is 1.15 × m/s

and % of uncertainty in speed =  2.07 × %

Explanation:

given data

mass = 45.9 gram = 0.0459 kg

speed = 200 km/hr = 55.5 m/s

uncertainty position Δx = 1 mm = m

to find out

speed of the golf ball and  % of speed of the golf ball

solution

we will apply here heisenberg uncertainty principle that is

uncertainty position ×uncertainty momentum ≥    ......1

Δx × ΔPx  ≥

here uncertainty momentum ΔPx = mΔVx

and uncertainty velocity = ΔVx

and h = 6.626 × Js

so put here all these value in equation 1

× 0.0459 × ΔVx =  

ΔVx = 1.15 × m/s

and

so % of uncertainty in speed = ΔV / m

% of uncertainty in speed =  1.15 ×  / 55.5

% of uncertainty in speed =  2.07 × %