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Question

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.


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Solution

Step 1: Given Information:

Mass of rifle, M=4 kg

Mass of bullet, m=50 g

Initial velocity of bullet, v=35 ms-1

Step 2: To find

Let Initial recoil velocity of gun = V

Step 3: Formula and solution

According to law of conservation of momentum,

total momentum before collision = total momentum after collision

Before firing, the velocity of gun and bullet is zero, so

After firing, momentum of gun = MV, momentum of bullet = mv

0=MV+mv MV=-mv V=-mvM V=-50×354×1000 V=-716 V=-0.4375 ms-1

The recoil velocity of the gun is -0.4365 ms-1. The negative sign shows that the recoil velocity will act opposite to the direction of motion of the bullet.


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