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velocity and the gun moves with velocitv . As no external force acts on the system,

so according to the principle of conservation of momentum,
Total momentum before firing
= Total momentum after firing

0 = MV+mv
Or -mv = MV

Or v = -MV/m Fig. 5.21

The negative sign shows that V and v are in opposite directions i.e., the gun gives a kick
in the backward direction or the gun recoils with velocity v. Further, as M>>m, so V<< v
i.e., the recoil velocity of the gun is much smaller than the forward velocity of the bullet.
(ii) While firing a bullet, the gun should be held tight to the shoulder. The recoiling
gun can hurt the shoulder. If the gun is held tightly against the shoulder, then the body
and the gun together will constitute one system. Total mass becomes large and the
recoil velocity becomes small.

(iii) When a man jumps out of a boat to the shore, the boat slightly moves away
from the shore. Initially, the total momentum of the boat and the man is zero. As the
man jumps from the boat to the shore, he gains a momentum in the forward direction.
To conserve momentum, the boat also gains an equal momentum in the opposite
direction. So the boat slightly moves backwards.
(iv) An astronaut in open space, who wants to return to the spaceship, throws
some object in a direction opposite to the direction of motion of the spaceship.
By doing so, he gains a momentum equal and opposite to that of the thrown object and
so he moves towards the spaceship.

(v) Rocket and jet planes work on the principle of conservation of momentum.
Initially, both the rocket and its fuel are at rest. Their total momentum is zero. For rocket
propulsion, the fuel is exploded. The burnt gases are allowed to escape through a
nozzle with a very high downward velocity. The gases carry a large momentum in the
downward direction. To conserve momentum, the rocket also acquires an equal
momentum in the upward direction and hence starts moving upwards.