Conservation of Momentum, a Totally Inelastic Collision

[mvl46566]

Homework Statement

A 950kg compact car is moving with the velocity ⃗v1 = 32 ˆx + 17 ˆy m/s. It
skids on an icy, frictionless patch and collides with a 450kg hay wagon
moving with velocity ⃗v2 = 12ˆx +14ˆy m/s. If the two stay together,
what is their velocity?

Homework Equations

m1v1 (initial) + m2v2 (initial) = vf (m1+ m2)

The Attempt at a Solution

I realize this is a totally inelastic collision and I need to use the above equation to solve. However, I don't know how to change the vector components into a number that can be plugged into the formula. I have tried adding the vector components of both velocities (x+x, y+y) but the answers I am getting do not sound right. I tried doing this because I figured if I know the numbers for the masses I can factor them out and have the vectors being added to together, but I don't think this is the solution. Please help!

 

[rl.bhat]

Show your calculations. Try this one.
m1*v1x + m2*v2x = (m1+m2)*vfx.
Similarly for y components.