A 3.50-g bullet has a muzzle velocity of 250 m/s when fired by a rifle with a weight of 25.0 N. (a) Determine the recoil speed of the rifle. m/s (b) If a marksman with a weight of 650 N holds the rifle firmly against his shoulder, determine the recoil speed of the shooter and rifle.

(a) 0.343 m/s

(b) 0.012 m/s

Explanation:

(a) From the question above,

MV = mv Equation 1

Where M = mass of the rifle, V = recoiling speed of the rifle, m = mass of the bullet, v = velocity of the bullet.

make V the subject of the equation

V = mv/M Equation 2

Given: m = 3.5 g = 0.0035 kg, v = 250 m/s, M = 25 N = 25/9.8 = 2.55 kg.

Substitute into equation 2

V = (0.0035×250)/2.55

V = 0.343 m/s.

(b) Similarly,

(M'+M)V' = mv Equation 3

Where M' = mass of the marksman, V' = recoiling speed of the shooter and rifle

make V' the subject of the equation

V' = mv/(M'+M) Equation 4

Given: m = 3.5 g = 0.0035 kg, v = 250 m/s, M = 25 N = 25/9.8 = 2.55 kg, M' = 650 N = 650/9.8 = 66.33 N

Substitute into equation 4

V' = (0.0035×250)/(66.33+2.55)

V' = 0.8125/68.88

V' = 0.012 m/s

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