Question

A rifle of mass M is initially at rest. A bullet of mass m is fired from the rifle with a velocity of v relative to the ground. What is the expression that gives the velocity of the rifle relative to the ground after the bullet is fired?

Answer 1

Answer:

$V_{rifle} = -\frac{mV_{bullet} }{M}$.

Explanation:

According to conservation of momentum, the momentum of rifle before fire is equal to the momentum of bullet after fire plus momentum of rifle after fire.

This in mathematics translates to.

$(M+m)v_{rifle-before-fire}=Mv_{rifle-after-fire}+mv_{bullet}$

rifle is stationary before fire so $v_{rifle-before-fire}=0$  this means that left side is 0.

$0=Mv_{rifle-after-fire}+mv_{bullet}$

solving for $v_{rifle-after-fire}$ in above gives us our answer.