# An Alternate Solution Using Conservation of Momentum

## Example 2: Finding the Velocity After an Inelastic Collision - Both Objects Initially Moving

Having both colliding objects moving before the collision introduces no major complications (just one additional term to deal with) to the solution, as shown below.

Two meatballs are speeding directly toward each other. One is a 4.0-kg meatball moving with a speed of 6.0 m/s, and the other has a mass of 2.0 kg and a speed of 4 m/s. If they collide inelastically, what will be the speed of the resulting 6.0 kg meatball immediately after the collision?

### Solution:

Since no external forces act on the two-meatball system (it is an "isolated system"), the total momentum of the system is conserved. The momentum before the collision is:

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

and the total system momentum after the collision is:

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

"Momentum is conserved" means:

p_{after} = p_{before}

so that:

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

and:

The 6.0-kg meatball has a velocity of about 2.7 m/s immediately after the collision.

*last update April 4, 2006 by JL Stanbrough*