Why Is My Calculation of Final Velocities in an Elastic Collision Incorrect?

[jubbly]

Homework Statement

Two carts with masses m1 = 0.8 kg and m2 = 1.2 kg are moving toward each other with
speeds v1 = 4.5 m/s and v2 = 3.8 m/s as shown in the diagram below. The two carts
collide elastically.

Some reason I'm getting too high of a value, don't know I'm doing wrong...

Homework Equations

momentum = m1v1 + m2v2 = m1vf1 + m2vf2

kinetic energy = .5m1v1^2 + .5m2v2^2 = .5m1vf^2 + .5 m1vf2^2

The Attempt at a Solution

So I found the momentum which came out to be -.96 = .8vf1 + 1.2vf2
Rearranged the equation to solve for vf2 = -(2/3)vf1 - .8
Then tried to find kinetic energy and got 8.1 + 10.83 = .4vf1^2 + .6vf2^2

Plugged in v2 and got 16.76 = .4vf1^2 + (4/15)vf1^2 + .64vf1 + .384
Subtracted 16.76 from both sides
Used quadratic equation

Came out with 13.5 m/s for vf1.

 

[Doc Al]

Then tried to find kinetic energy and got 8.1 + 10.83 = .4vf1^2 + .6vf2^2

Check the second term on the left hand side.

 

[jubbly]

Check the second term on the left hand side.

Fixed it a little, but still getting a pretty high number. Is that really the answer?

 

[Doc Al]

Fixed it a little, but still getting a pretty high number. Is that really the answer?

No. I got the same equation as yours, but got a lower answer.