Question

Two identical parties move towards each other with velocity $2V$ & $V$ respectively. What is the velocity of centre of mass?

Answer 1

Given:
$V_1=V(\uparrow )$
$V_2=2V(-\uparrow )$
$m_1=m_2=m$
Velocity of COM $\Rightarrow \overrightarrow{V_{CM}}=\frac{m_1\overrightarrow{V_1}+m_2\overrightarrow{V_2}}{m_1+m_2}$
$\Rightarrow \overrightarrow{V_{CM}}=\frac{mV(\uparrow )+m\left(2V\right)(-\uparrow )}{2m}$
$\Rightarrow \overrightarrow{V_{CM}}=\frac{V}{2}(-\uparrow )$