Question

A 6.00-g bullet has a muzzle velocity of 240 m/s when fired by a rifle with a weight of 20.0 N.

(a) Determine the recoil speed of the rifle.

If a marksman with a weight of 700 N holds the rifle firmly against his shoulder, determine the recoil speed of the shooter and rifle.

Answer 1

Acceleration due to gravity g = 10 m/s².

(a) Mass of bullet m1 = 6 g = 0.006 kg Velocity of bullet V1 = 240 m/s

Weight of rifle W = 20N.

Mass of rifle m2 = W/g = 20/10 = 2 kg.

From the conservation of momentum

m1 V1 = m2 V2

=> V2 = m1 V1 / m2 = (0.006 x 240)/2 = 0.72 m/s

Hence, the recoil speed of the rifle V2 = 0.72 m/s

b) Total weight of shooter and rifle W = 700 + 20 = 720 N

Then, total mass of shooter and rifle m2 = 720/10 = 72 kg

Again using conservation of momentum,

V2 = (0.006 x 240)/72 = 0.02 m/s.

Hence, the recoil speed of shooter and rifle V2 = 0.02 m/s.