Physics - Center of Mass Question with Solution | TestHub

In a perfectly inelastic collision, momentum is conserved. Let the initial velocities be ${\vec{v}}_1=v_0\hat{i}$ and ${\vec{v}}_2=v_0\hat{j}$. The masses are $m_1=m$ and $m_2=2m$. After collision, the combined mass $(m_1+m_2)=3m$ moves with a common velocity $\vec{V}$. By conservation of momentum: $m_1{\vec{v}}_1+m_2{\vec{v}}_2=(m_1+m_2)\vec{V}$. So, $m(v_0\hat{i})+2m(v_0\hat{j})=(m+2m)\vec{V}$. This gives $m{v}_0\hat{i}+2m{v}_0\hat{j}=3m\vec{V}$. Therefore, $\vec{V}=\frac{m{v}_0\hat{i}+2m{v}_0\hat{j}}{3m}=\frac{v_0}{3}(\hat{i}+2\hat{j})$.