Two cars collide at an intersection. One car has a mass of 1600 kg and is moving 8 m/s to the north, while the other has a mass of 1400 kg a

Yes i understand that as a Troll you feel the total need to say something snarky. 

I assume that Heureka also understands this. 

Yes I did notice your vector arrows, I'll have to add them to our very disorganised LaTex thread. :)

It is always great to get new commands.

I did not think that momentum and velocity were the same thing but the question asks for momentum and you answered with a velocity so I was confused. 

So does that mean that the combined momentum is     $$1.\bar{3}*3000 = 4000\;kg\;m/s$$

Well i am glad that you did not want to start something that you could not finish but if you make a spelling mistake perhaps you should not blame others.  Your computer cannot even defend itself. 

Solution

$$\small{\text{$\boxed{\vec{v}_1 = \vec{v}_2 = \dfrac {(m_1\cdot v_1 - m_2\cdot v_2 )}{ (m_1+ m_2 ) } } \quad\begin{array}{rcl}m_1 &=& 1400\ \mathrm{kg} \\v_1 &=& 12\ \frac{\mathrm{m} }{ \mathrm{s} } \end{array}\quad\begin{array}{rcl}m_2 &=& 1600\ \mathrm{kg} \\v_2 &=& 8\ \frac{\mathrm{m} }{\mathrm{s}} \end{array}$}}\\\\\\\small{\text{$\vec{v}_1 = \vec{v}_2 = \dfrac {(1400\cdot 12 - 1600\cdot 8 )}{ (1400+ 1600 ) } \ \dfrac{\mathrm{m} }{\mathrm{s}} $}}\\\\\small{\text{$\vec{v}_1 = \vec{v}_2 = \dfrac { 4000 }{ 3000 } \ \dfrac{ \mathrm{m}}{\mathrm{s}} = 1.3333\dots\ \dfrac{ \mathrm{m} }{\mathrm{s} } $}}\\\\\small{\text{$m_1\cdot \vec{v}_1 + m_2\cdot \vec{v}_2 = 1400 * 1.3333\dots \;+ \;1600 * 1.3333\dots =\; 4000\ \frac{\mathrm{kg}\cdot \mathrm{m}}{\mathrm{s}}$}}\\\end{array}$}}\\
\small ${\text{Velocity of combined cars = 1.33\overline 3(\dot 3)\; \dfrac{m}{s}\; south.}$$

Letex code stolen from Heureka _{(and vastly improved)}

You have presented this beautifully Nauseated but

I see NO IMPROVEMENT on Heureka's presentation.

PLUS Heureka knows how to spell LaTex properly !

Is momentum and velocity the same thing?  

I see NO IMPROVEMENT on Heureka's presentation.

There isn’t. The only difference is the use of arrow vectors.

I’m a troll, so my posts aren’t really complete without (a) snarky comment(s).

PLUS Heureka knows how to spell LaTex properly !

 Considering his proficiency, I’m sure he does. However, I was using a company computer, and the command “Letex” is used to initiate Schematron-based XHTML table validation scripts for creating LaTeX formula images. D**k, a  company programming troll, used “LaTex” as a command to start a process to produce extra-large latex rubbers. The demand for these is small and I didn’t want to start something I couldn't finish.

Is momentum and velocity the same thing?

No. They are two different quantities.

Velocity is the speed with the direction.

Momentum is the product of mass and its velocity.

. . . the question asks for momentum and you answered with a velocity so I was confused.

 Actually, I answered with both momentum and velocity. Though not asked for, I included velocity because in dynamical systems, a mass’s position in space and rate of change of position in space are almost always useful pieces of information. This is especially so in situations involving vehicle crashes.

. . . but if you make a spelling mistake perhaps you should not blame others. Your computer cannot even defend itself.

True, but it doesn’t need to. I was blaming D**k, the programming troll. BTW my name is D**k, so either way, the blame is where it belongs. :)