A 10g bullet is shot from a 5kg gun with a velocity of 400m/s.What is the speed of recoil of the gun?
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Mass of bullet, m = 10 g = 0.01 kg
Mass of gun, M = 5 kg
Velocity of bullet, v = 400 m/s
Recoil velocity of the gun, V = ?
Initially the gun and bullet were at rest, so, the initial momentum of the system is, Pi = 0
After firing the momentum of the system = momentum of gun + momentum of bullet
=> Pf = MV + mv
=> Pf = 5V + (0.01)(400)
=> Pf = 5V + 4
By conservation of momentum,
Pf = Pi
=> 5V + 4 = 0
=> V = -4/5 = -0.8 m/s
Thus, the recoil velocity of the gun is oppositely directed with respect to the velocity of the bullet.
The speed of recoil of the gun is 0.8 m/s.
Explanation:
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