Question

A rifle with a weight of 25 N fires a 5.5-g bullet with a speed of 280 m/s

(a) Find the recoil speed of the rifle.
___________m/s

(b) If a 725-N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle.
___________m/s

Answer 1

here,

the mass of bullet , m1 = 5.5 g = 0.0055 kg

weight of rifle , W2 = 25 N

the mass of rifle , m2 = W2 /g

m2 = 2.55 kg

a)

the initial speed of bullet , v1 = 280 m/s

let the final recoil velocity be v2

using conservation of momentum

0 = m1 * v1 + m2 * v2

0 = 0.0055 * 280 + 2.55 * v2

v2 = - 0.604 m/s

the final recoil speed is 0.604 m/s

b)

mass of man , m3 = 725 /g = 73.9 kg

let the final recoil velocity be v3

using conservation of momentum

0 = m1 * v1 + (m2 + m3) * v3

0 = 0.0055 * 280 + (2.55 + 73.9) * v3

v3 = - 2.01 * 10^-2 m/s

the final recoil speed is 2.01 * 10^-2 m/s