A bullet of mass 50 g is fired from a gun of mass 4kg. If velocity of the bullet just after firing is 40ms-1, what is the recoil velocity of the gun?
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Answer:
✯Required Question:
- From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m/s. Calculate the initial recoil velocity of the rifle.
✯To Find:
- what is the recoil velocity of the gun?
✯Solution:
Mass of the rifle (m1) = 4 kg
Mass of the bullet (m2) = 50 g = 0.05 kg
Recoil velocity of the rifle = v1
A bullet is fired with an initial velocity (v2) = 35 m/s
Initially, the rifle is at rest.
Thus, its initial velocity (v) = 0
Total initial momentum of the rifle and bullet system
⇒ (m1+m2) × v = 0
The total momentum of the rifle and bullet system after firing
= m1v1 + m2v2
= (4 × v1 ) + (0.05 × 35)
= 4v1 + 1.75
According to the law of conservation of momentum
Total momentum after the firing = Total momentum before the firing
4v1 + 1.75 = 0
v1= -1.75 / 4
v1 = – 0.4375 m/s
The negative sign indicates that the rifle recoils backwards with a velocity of 0.4375 m/s.
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