How Do Collisions Affect Momentum in Physics Problems?

[hshphyss]

Can anyone help me with these two problems? Thank-you

1.) Two carts with masses of 15.5 kg and 6.0 kg, respectively, move in opposite directions on a frictionless horizontal track with speeds of 7.0 m/s and 2.0 m/s, respectively. The carts stick together after colliding head-on. Find the final speed of the two carts.

For this one, I know one of the velocities has to be negative, but which one? Does it matter?

2.) A 1.80 kg skateboard is coasting along the pavement at a speed of 7.0 m/s when a 0.400 kg cat drops from a tree vertically downward onto the skateboard. What is the speed of the skateboard-cat combination.

For this problem I know that the cat's acceleration will be -9.8, is that correct?

 

[ChaoticLlama]

Can anyone help me with these two problems? Thank-you
1.) Two carts with masses of 15.5 kg and 6.0 kg, respectively, move in opposite directions on a frictionless horizontal track with speeds of 7.0 m/s and 2.0 m/s, respectively. The carts stick together after colliding head-on. Find the final speed of the two carts.
For this one, I know one of the velocities has to be negative, but which one? Does it matter?

I don't believe it matters which direction you choose to be positive and negative, as long as you are consistent throughout the question.

In conservation of momentum, theTotal initial momentium is equal to the total final momentum, and since we are dealing with two bodies, we have

M1V1o + M2V2o = (M1 + M2)Vf
(15.5Kg)(7m/s) + (6.0Kg)(-2m/s) = (21.5Kg)Vf
Vf = 4.49m/s