Momentum, collision of two cars problem

[Erenjaeger]

Homework Statement

A 3.0 kg cart moving to the right with a speed of 1.0 m/s has a head-on collision with a 5.0 kg cart that is initially moving to the left with a speed of 2.0 m/s. After the collision, the 3.0 kg cart is moving to the left with a speed of 1.0 m/s. What is the final velocity of the 5.0 kg cart?

Homework Equations

P=mv

The Attempt at a Solution

I took the initial momentum of both cars and added them for the total initial momentum which was 3⋅1+5⋅2 = 13 kg m/s
so because of the conservation of momentum P_f=P_o so the final total momentum will have to be 13 kg m/s also.
so P_ftotal = P_{car 1} + P_{car 2}
car 1 is now moving to the left with a velocity of 1m/s so its momentum is still 3 kg m/s
so 13=3+P_{car 2}
and we know the mass of car 2 is 5kg so 13=3+2⋅V and we see the momentum of car 2 would have to be 10 kg m/s to result in a final total momentum of 13kg m/s so wouldn't the velocity have to be 2m/s ?? but on the answer sheet it says the final velocity is 0.8m/s to the left.

 

[gneill]

I took the initial momentum of both cars and added them for the total initial momentum which was 3⋅1+5⋅2 = 13 kg m/s

Are both cars moving in the same direction? Remember that momentum is a vector: it has both magnitude and direction.

 

[Erenjaeger]

Are both cars moving in the same direction? Remember that momentum is a vector: it has both magnitude and direction.

Oh true, right so using the same method but assuming movement to the right is in the positive direction and movement to the left is in the negative direction, I should arrive at the correct answer ?

 

[haruspex]

Oh true, right so using the same method but assuming movement to the right is in the positive direction and movement to the left is in the negative direction, I should arrive at the correct answer ?

How you assign positive and negative for each velocity is up to you. You should get the right answer as long as you are consistent. It usually helps to achieve consistency if you pick one positive direction for all velocities on a given axis.

 

[gneill]

Oh true, right so using the same method but assuming movement to the right is in the positive direction and movement to the left is in the negative direction, I should arrive at the correct answer ?

Sure, that would work. It's usually best to decide on your coordinate system before you start doing calculations.

 

[Kuzon]

No offense. But you haven't really tried to address the problem at play here in an optimal manner! What is the formula you initially tried to use in order to solve the problem aside from P=mv?