REMEMBER ONE THING – THE MOVEMENT OF SOME BODY AT REST OR THE CHANGE OF SPEED OF ANY OBJECT HAVE NO CONCERN WITH INTERNAL FORCES BUT ARE ALWAYS CONCERNED WITH EXTERNAL FORCES , AND NOT ONLY FORCES THE NET FORCE IS THE ONE WHICH BRING OUT CHANGES , SO , ALWAYS REMEMBER.

Well in these types of problems first we need to consider some system related to the question on which we will apply the laws.

In this question we will consider the gun , the bullet , and the person shooting , all these objects as one system.

As we know that the momentum of a system is always conserved when no external force is applied on it , by law of conservation of momentum and in the context of Newton’s third law we will solve the problem.

As the bullet possesses some mass and the gun also has mass which is much larger than that of bullet , so as the bullet leaves the barrel(the long straight hollow rod from where bullet leaves) of the gun it has large velocity and so the momentum of the bullet increases hence as to conserve the momentum as by law of conservation of momentum the gun should have some velocity as calculated mathematically and in the opposite direction of that of the bullet.

Mathematically,

As you can see the velocity of the gun(v_g) comes out in the negative direction or opposite direction of that of the bullet(v_b) , so , that is why the gun recoils.

ADDITIONAL INFORMATION – The bullet in the gun is driven by the gases formed inside the gun , as gases expand due to less space so they exert equal amount of force on the gun also hence the gun recoils and the bullet travels faster due to mass differences.

By Newton’s third law the action is the gases act on gun so we experience recoil and the reaction is our stability or to absorb the thrust of the gun.