Center of Mass Velocity in Multiple Dimmensions

[tummbacoco]

I was doing some practice problems to become more familiar with the Center of Mass Velocity and I came across this one from (Noted in the picture) Engineering at Illinois, that relates the velocity of the center of mass in both the x and y direction, however I don't quit understand the answer.

V_CM = (M₁V₁ + M₂V₂)/ M_total

Since this is the case V_CM should equal 2.4, but the question asked for the velocity in the x and y direction

Since only one object is moving in the x-direction shouldn't that be the V_CM for the x-direction??
Why would V_CM (x-direction) = Momentum in the x-direction? How would one go about calculating V_{CM for individual dimensions?} Thanks!

 

[BvU]

Since only one object is moving in the x-direction shouldn't that be the VCM for the x-direction??

No. As you see in the formula,

VCM = (M₁V₁ + M₂V²)/ Mtotal

There are factors $m_1/m_{\rm total}$ and $m_2/m_{\rm total}$

Why would VCM (x-direction) = Momentum in the x-direction?

It isn't. $v_{\rm} \;m_{\rm total}$ is the momentum.

 

[Ibix]

How would one go about calculating VCM for individual dimensions?

The easiest way to do it is to remember that velocity is a vector, which you seem to have forgotten when you got your 2.4m/s answer.