Consider a system of two particles: ball A with a mass m is moving to the right a speed 2v and ball B with a mass 3m is moving to the left at a speed v. In the time interval before the two balls collide, what is the magnitude and the direction of the velocity of the center of mass of this system?

Given that,

System of two particle

Ball A has mass

Ma = m

Ball A is moving to the right (positive x axis) with velocity of

Va = 2v •i

Ball B has a mass

Mb = 3m

Ball B is moving to left (negative x axis) with a velocity of

Vb = - v •i

Velocity of centre of mass Vcm?

Velocity of centre of mass can be calculated using

Vcm = 1/M ΣMi•Vi

Where M is sum of mass

M = M1 + M2 + M3 + ...

Therefore,

Vcm=[1 / (Ma + Mb) ] * (Ma•Va + Mb•Vb

Rearranging for better understanding

Vcm = (Ma•Va + Mb•Vb) / (Ma + Mb)

Vcm = (m•2v + 3m•-v) / (m + 3m)

Vcm = (2mv - 3mv) / 4m

Vcm = - mv / 4m

Vcm = - v / 4

Vcm = - ¼V •i