The muzzle velocity of a rifle bullet is 800. m⋅ s −1 m⋅s−1 along the direction of motion. If the bullet weighs 27.0 g g , and the uncertainty in its momentum is 0.200 % % , how accurately can the position of the bullet be measured along the direction of motion?

1.98 × 10⁻³³m

Explanation:

It is given that,

Mass of the bullet, m = 27 g = 0.027 kg

Velocity of bullet, v = 800 m/s

The uncertainty in momentum is 0.20%. The momentum of the bullet is given by :

Uncertainty in momentum is,

We need to find the uncertainty in position. It can be calculated using Heisenberg uncertainty principal as :

the maxium height is 34m/s