Recall that the blocks can only move along the x axis. The x components of their velocities at a certain moment are v1x and v2x. Find the x component of the velocity of the center of mass (vcm)x at that moment. Keep in mind that, in general: vx=dx/dt.

Vcm = m1v1 + m2v2 / m1 + m2

Explanation:

The distance of centre of mass Xcm can be taken by taking mass moments about the origin.

(m1 + m2)Xcg = m1x1 + m2x2

Xcm = m1x1 + m2x2 / m1 + m2

Differentiating Xcm = m1x1 + m2x2 / m1 + m2 with respect to time t, will give us the velocity of the centre of mass.

I have attached a diagram showing said differentiation.

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