Question

A rifle bullet of mass 60.0 g leaves the muzzle of a rifle with a velocity of 2.8 x 10² m/s. If
the rifle has a mass of 3.1 kg, with what velocity will it recoil?

Answer 1

So, the final velocity of the riffle is approximately 5.42 m/s in the opposite direction from the bullet. (Ignore the negative signs, because it just show the direction)

[See on the attached picture to know how to solve it !]

Introduction

Hi ! Here I will help you to solve the problem about the law of conservation of momentum. Momentum is the condition when an object with mass m moves with velocity v. The momentum of an object will be conserved when it causes a velocity on another object after the collision. Like in the example, when the bullet exits the rifle, it will cause a jolt to the riffle in a direction that opposes the movement of the bullet. Its a normal condition that the velocity of the riffle will have negative (-) value, if we look at the direction of the bullet's motion.

Formula Used

Equations that use the law of conservation of momentum equations depend on the state of the plant. However, in this case, the formula used is :

$\boxed{\sf{\bold{m_b \cdot v_b + m_r \cdot v_r = m_b \cdot (v_b)' + m_r \cdot (v_r)'}}}$

With the following condition:

• $\sf{m_b}$ = mass of the bullet (kg)
• $\sf{v_b}$ = initial velocity of the bullet (m/s)
• $\sf{m_r}$ = mass of the riffle (kg)
• $\sf{v_r}$ = initial velocity of the riffle (m/s)
• $\sf{(v_b)'}$ = final velocity of the bullet (m/s)
• $\sf{(v_r)'}$ = final velocity of the riffle (m/s)

Solution

We know that :

• $\sf{m_b}$ = mass of the bullet = 60 gr = 0.06 kg
• $\sf{v_b}$ = initial velocity of the bullet = 0 m/s >> Assume the bullet is still inside the riffle.
• $\sf{m_r}$ = mass of the riffle = 3.1 kg
• $\sf{v_r}$ = initial velocity of the riffle = 0 m/s >> The riffle at the rest condition.
• $\sf{(v_b)'}$ = final velocity of the bullet = $\sf{2.8 \times 10^2}$ m/s.

What was asked ?

• $\sf{(v_r)'}$ = final velocity of the riffle = ... m/s

Step by step :

[See on attached picture]

Conclusion

So, the final velocity of the riffle is approximately 5.42 m/s in the opposite direction from the bullet.