Question

A bullet mass 30g is fired from a gun of mass 2kg. The muzzle speed of the bullet is 100m/s. Find the recoil speed of the gun

Answer 1

Given A bullet mass 30 g is fired from a gun of mass 2 kg. The muzzle speed of the bullet is 100 m/s. We need to find the recoil speed of the gun.

Let mass of bullet be m = 30 g = 0.03 kg

   Mass of the gun be M = 2 kg

  Speed of the bullet or velocity = v = 100 m /s

Initial momentum of the bullet and gun is 0

Final momentum = momentum of gun + momentum of bullet

 We know conservation of linear momentum is given by

         M V  + m v = 0

          V = - (m v) / M

         V = - (0.03 x 100) / 2

         V = - 3 /2

         V = - 1.5 m / s

The recoil speed of the gun is - 1.5 m / s

Answer 2

Mass of the Gun = 2 kg.

Speed of the Gun = v

Mass of the bullet = 30 g = 0.03 kg.

Speed of the Bullet = 100 m/s.

Using the law of the conservation of the momentum,

 Total Momentum before and after the collision is constant, if no net force acts on a body.

Since, there is no net force acting on the body.

∴  Mass of the bullet × Velocity of the bullet = Mass of the Gun × Velocity of the Gun

∴ 2 × v = 0.03 × 100

∴ v = 3/2

∴ v = 1.5 m/s.

It is the required velocity of the bullet in opposite direction.

Hope it helps.