# An Alternate Solution Using Conservation of Momentum

## Example 3: Bullet and Block

A bullet with a mass of 0.020 kg collides inelastically with a wooden block of mass 2.5 kg, initially at rest. After the collision, the bullet + block has a speed of 1.2 m/s. What was the initial speed of the bullet?

### Solution:

This problem is essentially the same as Example 1. Since no external forces act on the bullet + block system, the system's total momentum is conserved. The system's momentum before the collision is:

p_{before} = m_{1}v_{1} + m_{2}v_{2} = m_{1}v_{1}

and the system's momentum after the collision is:

p_{after} = (m_{1} + m_{2})v

If momentum is conserved, then:

p_{after} = p_{before}

(m_{1} + m_{2})v = m_{1}v_{1}

We want to know v_{1}, so:

The velocity of the bullet immediately before the collision was 150 m/s.

*last update April 4, 2006 by JL Stanbrough*