What are the velocities of the carts after a perfectly elastic collision?

[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.

Homework Equations

1/2m₁v_i1² + 1/2m₂v_i2² = 1/2m₁v_1f² + 1/2m₂v_2f²

m1vi1 + m2v2i = m1v1f + m2v2f

The Attempt at a Solution

I plugged in all of the numbers.

For momentum I got
2= V1f + 2 V2f

For kinetic energy I got
4 = V1f² + 2V2f²

Next I solved for V1f and plugged it into the equation.

I just need some confirmation that my answer is right.

It doesn't seem correct.

I got:
V2f = 2
V1f = -2

 

[Hootenanny]

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.

Homework Equations

1/2m₁v_i1² + 1/2m₂v_i2² = 1/2m₁v_1f² + 1/2m₂v_2f²

m1vi1 + m2v2i = m1v1f + m2v2f

The Attempt at a Solution

I plugged in all of the numbers.

For momentum I got
2= V1f + 2 V2f

For kinetic energy I got
4 = V1f² + 2V2f²

Next I solved for V1f and plugged it into the equation.

I just need some confirmation that my answer is right.

It doesn't seem correct.

I got:
V2f = 2
V1f = -2

You could check your answers yourself. Do they satisfy both the kinetic energy and momentum equations?

 

[southernbelle]

No, they don't. You're right that was an easy way to check myself.