Answer to Question #88214 in Mechanics | Relativity for Amoo Emmanuel

Question

A bullet of mass 15g is fired from a riffle with a velocity 100m/s. If the mass of the riffle is it kg. What is the recoil velocity of the riffle?

Answer 1

We can find the recoil velocity of the riffle from the law of conservation of momentum (the total initial momentum of the riffle and the bullet is zero, because they both are initially at rest):

$$p_{total(initial)} = p_{total(final)},$$ $$p_{total(initial)} = 0,$$ $$M_{riffle}v_{riffle} + m_{bullet}v_{bullet} = 0,$$ $$M_{riffle}v_{riffle} = -m_{bullet}v_{bullet},$$ $$v_{riffle} = -\dfrac{m_{bullet}v_{bullet}}{M_{riffle}}.$$

From this formula we can calculate the recoil velocity of the riffle. Unfortunately, the mass of the riffle isn't specified in the condition of the question. Let's take $M_{riffle} = 4.0 kg$, for example. Then, we get:

$$v_{riffle} = -\dfrac{0.015 kg \cdot 100 \dfrac{m}{s} }{4.0 kg} = -0.375 \dfrac{m}{s}.$$

The sign minus indicates that the recoil velocity of the riffle directed in the opposite direction to the velocity of the bullet.

Answer:

$v_{riffle} = 0.375 \dfrac{m}{s}.$