Conservation of momentum in one direction (add or subtract?)

[Chris Jarvis]

Homework Statement

Hey everyone! I'm new to these forums so I apologize in advance if I do something wrong! I just had a quick question about the momentum in one direction equation m_1v_1o +/- m_2v_2o = m_1v_1f +/- m_2v_2f; I'm just not sure when I'm supposed to add these values and when I'm supposed to subtract them. I thought it had to do with the objects vector, but there is conflicting questions in my lesson (I think at least). I'm doing an online course so I don't really have a teacher to ask lol
For example:
Football player 1 with a mass of 110kg is moving at 8.0m/s when he crashes into football player 2 with a mass of 105kg, moving at 12 m/s [N]. During the tackle football player 1 holds onto football player 2, giving them the same velocity after 0.30s.
a) Find the final velocity of each player after collision

In a Physics experiment, a 1.2kg cart1 is moving at 3.2m/s [R], when it collides with a 1.8kg cart 2 which is moving at 5.8m/s[L]. After the collision cart1 is moving at 7.6m/s[L].Find the velocity for cart2 after the collision.

Homework Equations

m_1v_1o + m_2v_2o= (m_1+m_2)v_f
m_1v_1o - m_2v_2o = m_1v_1f + m_2v_2f

The Attempt at a Solution

So for the football one my book shows;
Let [N] be positive
P_to=P_tf
m_1v_1o + m_2v_2o= (m_1+m_2)v_f
(110kg)(-8.0m/s)+(105kg)(12m/s)= (110kg +105kg)v_f
v_f=1.77m/s[N]

For the Physics experiment one:
P_1o-P_2o=P_1f+P_2f
Let [R] be positive;
m_1v_1o - m_2v_2o = m_1v_1f + m_2v_2f
(1.2kg)(3.2m/s)-(1.8kg)(5.8m/s)=-(1.2kg)(7.6m/s)+(1.8kg)v_2f
-6.6kgm/s= -9.12kgm/s + (1.8kg)v_2f
v_2f= 1.4m/s [R]
So Is it because the two forces are combining in the first that you add? and in the second one they bounce away so you subtract?
Sorry if this is a really simple question, I haven't done physics in almost 8 years!
Thank you in advance!

 

[Doc Al]

Is there a reason most of your text is struck out? Did you still have a question?

 

[theodoros.mihos]

Put (+) everywhere and use vector direction to see the correct sign.

 

[Chris Jarvis]

Hey sorry everyone I didn't respond I went on vacation and dint have internet but i figured it out thank you both!