According to Heisenberg uncertainty principle,
Δx.Δv=h4πm
Δx=uncertainty in position
Δv=uncertainty in velocity
h=planck's constant
m=mass of particle.
Uncertaintyin the position:
Given:Mass of golf ball=40 g
Speed of golf ball=45m/s
accuracy in speed=2%
The uncertainty in the speed is 2%,i.e.,Δv=45×2100=0.9ms−1
According to Heisenberg uncertainty principle,
Δx.Δv=h4πm
Δx=h4πmΔv
Δx=6.626×10−34Js4×3.14×(40g×10−3kg g−1)×(0.9 ms−1)
This is nearly ∼1018 times smaller than the diameter of a typical atomic nucleus. As we know, for large particles,the uncertainty principle sets no meaningful limit to the precision of measurements.
Final Answer: uncertainty in position is 1.46×10−33m