# Perfectly elastic collision

by southernbelle
Tags: collision, elastic, perfectly
 P: 35 1. The problem statement, all variables and given/known data 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. 2. Relevant equations m1vi1 + m2vi2 = m1v1f + m2v2f 1/2m1vi12 + 1/2m2vi22 = 1/2m1v1f2 + 1/2m2v2f2 3. 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!!
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P: 40,278
 Quote by southernbelle 3. 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?
 P: 35 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
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P: 40,278

## Perfectly elastic collision

 Quote by southernbelle 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.

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