Collision of Two Cars: Calculating Velocity

[VelvetRebel]

Homework Statement

A 850 kg car is traveling west at 25.0 m/s when it collides with a 1050 kg car that was initially traveling north at 10.5 m/s. The cars lock together, and eventually skid to a stop.
What is the velocity of the cars immediately after the collision?

Homework Equations

p_i=p_ix i + p_iy j + p_iz k

The Attempt at a Solution

I got an answer but I'm not sure if it is correct. I just need someone to verify if what I did is correct.
Here's what I did:
I found p_i using the equation above and then took the magnitude of that to find p_f as shown below:

(-(850 kg)(25.0 m/s) i)² + ((1050 kg)(10.5 m/s) j)²=p_f²

I then took the p_f value and set that equal to the total mass times the velocity:

2.39 x 10⁴ kg*m/s=(850 kg + 1050 kg)v

I then solved for v to get the following:

v=12.6 m/s

 

[rl.bhat]

Your answer is correct.