A25 gram bullet is fired from a gun with a speed of 230 m/s. if the gun has a mass of 0.9 kg what is the recoil speed of gun ?

Given data:

mass of the bullet (m) = 25 g = 0.025 kg,

mass of the gun    (M) = 0.9 kg,

speed of the bullet (v) =230 m/s,

speed of the bullet (V) = ?

From the given data it is clear that, the momentum is conserved. According to "law of conservation of momentum" the total momentum before and after the collision is equal.

In this problem the momentum before collision (bullet+gun) is zero.

Therefore, after the gun fires a bullet, the momentum must be zero.

Mathematically,

          M × V + m × v = 0

           where,

                     M × V = momentum of the gun

                     m × v = momentum of the bullet

            (0. 9 × V) + (0.025 × 230) = 0

             0.9 V = -5.75

                    V = -5.75/0.9

                        = -6.39 m/s  

The gun recoils with a speed of 6.39 m/s