Question

explain why the velocity of a recoiling gun is lower than that of the eject bullet

Answer 1

This fact can be explained using law of conservation of momentum. Which is given by  

Total momentum of gun and bullet before fire = Total momentum of gun and bullet after fire

Left hand side will be zero because velocity of both bullet and gun is zero before firing so,

                                                 0 = mv’ + Mv

                                                 MV = -mv’

Negative sign shows that gun and bullet will move in the opposite direction.

As the mass of the gun is very high as compared to bullet so, velocity of gun will be less than bullet to conserve the momentum.

Answer 2

Answer:

I think you want to ask why the recoil velocity of the gun is less than that of the bullet.

The mass of the bullet and the mass of the gun have a vast difference. The bullet may leave the gun with a lot of force, but the difference between the gun's mass and the bullet's mass is what makes the recoil  velocity of the gun lower than that of the bullet.

Hope it helps you.