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 and is moving 12 m/s to the south. What is their combined momentum?

Guest Feb 18, 2015

#4**+5 **

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.

Melody
Feb 18, 2015

#1**+5 **## 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)}

Nauseated
Feb 18, 2015

#2**+5 **

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?**

Melody
Feb 18, 2015

#3**0 **

*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.

Nauseated
Feb 18, 2015

#4**+5 **

Best Answer

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.

Melody
Feb 18, 2015

#5**0 **

*. . . 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. :)

Nauseated
Feb 18, 2015