Question 3
From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m $s^{- 1}$ . Calculate the initial recoil velocity of the rifle.

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Solution

Mass of the rifle, $m_{1} = 4$ kg
Mass of the bullet, $m_{2} = 50 g = 0.05$ kg
Recoil velocity of the rifle $= v_{1}$
Bullet is fired with an initial velocity, $v_{2} = 35 m s^{- 1}$
Initially, the rifle is at rest.
Thus, its initial velocity, v= 0
Total initial momentum of the rifle and bullet system $= (m_{1} + m_{2}) v = 0$
Total momentum of the rifle and bullet system after firing:
$= m_{1} v_{1} + m_{2} v_{2} = 0.05 \times 35 = 4 v_{1} + 1.75$
According to the law of conservation of momentum:
Total momentum after the firing = Total momentum before the firing $4 v_{1} + 1.75 = 0$
$v_{1} = - \frac{1.75}{4} = - 0.4375 m s^{- 1}$
The negative sign indicates that the rifle recoils backwards with a velocity of 0.4375 $m s^{- 1}$

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Question 3 From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 ms−1 . Calculate the initial recoil velocity of the rifle.

Question 3
From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m $s^{- 1}$ . Calculate the initial recoil velocity of the rifle.