What Are the Final Velocities in a Perfectly Elastic Collision Problem?

[southernbelle]

Homework Statement

In an isolated system, cart1 (with mass = 1 kg and vi1 = 2) has a perfectly elastic collision with cart2 (with mass = 2 kg and vi2 = 0). Find the velocity of cart1 and the velocity of cart2 after the collision.
I have to solve this using kinetic energy and momentum equations.

Homework Equations

m1vi1 + m2vi2 = m1v1f + m2v2f
1/2m1vi1² + 1/2m2vi2² = 1/2m1v1f² + 1/2m2v2f²

The Attempt at a Solution

I have gotten to this point:
2= V1F + 2V2F
4= V1F2 + 2V2F

but I cannot get the numbers to work out correctly.
Using another equation I know that V1f = 2/3 and V2f = 4/3

I am doing substitution wrong or something.
Please help!

 

[Doc Al]

The Attempt at a Solution

I have gotten to this point:
2= V1F + 2V2F

This makes sense.

4= V1F2 + 2V2F

How did you get this?

 

[southernbelle]

I got that by solving the kinetic energy equation.
I mutiplied both sides by 2 to get rid of the halves.

It is actually supposed to read:

4 = Vif^2 + 2V2f^2

 

[Doc Al]

It is actually supposed to read:

4 = Vif^2 + 2V2f^2

That's good.

Take the first equation and solve for one of your variables. Then substitute that into the second equation. Solve the quadratic.