Two Cars Collision

[nasi112]

I took this question previously. My colleagues got [math]2.7 \ m/s[/math], but I got [math]2.1 \ m/s[/math]
Here how I did it.

momentum = mass x velocity

let us call the two vectors [math]\vec{A}[/math] and [math]\vec{B}[/math]
resultant of momentum = [math]|\vec{A} + \vec{B}| = \sqrt{(2 \cdot 2)^2 + (4 \cdot 3)^2} = 4\sqrt{10}[/math]
velocity [math] = \frac{4\sqrt{10}}{m_1 + m_2} = \frac{4\sqrt{10}}{2 + 4} = 2.1 \ m/s[/math]
Did I do anything wrong in my calculations?

 

[Romsek]

You should get used to using common labeling. Ignoring units we have

[MATH] m_1 v_1 + m_2 v_2 = m_f v_f = (m_1 + m_2)v_f\\ 2(2,0) + 4(0,3) = 6 v_f\\ (4,12) = 6v_f\\ v_f = \left(\dfrac 2 3,~2\right)\\ \|v_f\| = \left(\left(\dfrac 2 3\right)^2+2^2\right)^{\frac 1 2} = \\ \sqrt{\dfrac{40}{9}} \approx 2.1 [/MATH]

 

[nasi112]

Thanks Romsek. You made my day.