Block A, with a mass of 4.0 kg, is moving with a speed of 2.0 m/s while block B, with a mass of 8.0 kg, is moving in the opposite direction with a speed of 3.0 m/s. The center of mass of the two block system is moving with velocity of?

Consider velocity to the right as positive.

First mass:

m₁ = 4.0 kg

v₁ = 2.0 m/s to the right

Second mass:

m₂ = 8.0 kg

v₂ = - 3.0 m/s to the left

Total momentum of the system is

P = m₁v₁ + m₂v₂

= 4*2 + 8 * (-3)

= - 16 (kg-m) / s

Let v (m/s) be the velocity of the center of mass of the 2-block system.

Because momentum of the system is preserved, therefore

(m₁+m₂) v = - 16

(4+8 kg) * (v m/s) = - 16 (kg-m) / s

v = - 1.333 m/s

Answer:

The center of mass is moving at 1.33 m/s to the left.