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.

 

[Nickie]

Your approach to solving this problem seems correct. It is possible that there may be a calculation error or a mistake in setting up the equations. It may be helpful to double check your calculations and equations to ensure accuracy. Additionally, it may be helpful to check if the values given in the problem are correct and if there are any other factors that could affect the final result. If you are still getting a significantly different value, it may be helpful to seek assistance from a teacher or tutor for further clarification.