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?