Physics - Center of Mass Question with Solution | TestHub

The velocity of $m_1$ after impulse is ${\vec{v}}_1={\vec{J}}_1/m_1=(15\hat{i}+20\hat{j})\text{ m/s}$. The velocity of $m_2$ after impulse is ${\vec{v}}_2={\vec{J}}_2/m_2=(-6\hat{i}-8\hat{j})/2=(-3\hat{i}-4\hat{j})\text{ m/s}$. The velocity of the center of mass is ${\vec{V}}_{CM}=\frac{m_1{\vec{v}}_1+m_2{\vec{v}}_2}{m_1+m_2}=\frac{1(15\hat{i}+20\hat{j})+2(-3\hat{i}-4\hat{j})}{1+2}=\frac{(15-6)\hat{i}+(20-8)\hat{j}}{3}=\frac{9\hat{i}+12\hat{j}}{3}=(3\hat{i}+4\hat{j})\text{ m/s}$. The speed of the center of mass is $|{\vec{V}}_{CM}|=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\text{ m/s}$. The correct answer is 5.