Physics - Center of Mass Question with Solution | TestHub

The velocity of the center of mass of the system is:

$${\vec{V}}_{COM}=\frac{m_1{\vec{v}}_1+m_2{\vec{v}}_2}{m_1+m_2}$$

Substituting the values:

$${\vec{V}}_{COM}=\frac{2(3\hat{i}+2\hat{j})+3(2\hat{i}+4\hat{j})}{2+3}=\frac{12\hat{i}+16\hat{j}}{5}=(2.4\hat{i}+3.2\hat{j})\text{ m/s}$$

The magnitude of the velocity of the center of mass is:

$$|{\vec{V}}_{COM}|=\sqrt{(2.4{)}^2+(3.2{)}^2}=\sqrt{5.76+10.24}=\sqrt{16}=4\text{ m/s}$$

The magnitude of the velocity of the center of mass is 4 m/s.