As depicted in the figure, two blocks of masses m_1 and m_2 are...

Initial velocity of block $m_1$, $v_1 = 0$.

Initial velocity of block $m_2$, $v_2 = v_0$.

The velocity of the centre of mass of the system is given by:

$v_{cm} = \dfrac{m_1 v_1 + m_2 v_2}{m_1 + m_2}$

Substituting the values:

$v_{cm} = \dfrac{m_1(0) + m_2(v_0)}{m_1 + m_2}$

$v_{cm} = \dfrac{m_2 v_0}{m_1 + m_2}$

Since there is no net external force acting on the system in the horizontal direction after the impulse, the velocity of the centre of mass remains constant.