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(C) The velocity of the center of mass $\vec{V}_{cm}$ is given by the formula: $\vec{V}_{cm} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2}{m_1 + m_2}$ Given:

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$5 \ \hat{i} + \frac{25}{7} \ \hat{j}$

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(C) The velocity of the center of mass $\vec{V}_{cm}$ is given by the formula: $\vec{V}_{cm} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2}{m_1 + m_2}$ Given: $m_1 = 200 \ g$,$m_2 = 500 \ g$,$\vec{v}_1 = 10 \ \hat{i} \ m/s$,$\vec{v}_2 = 3 \ \hat{i} + 5 \ \hat{j} \ m/s$. Substituting the values: $\vec{V}_{cm} = \frac{200(10 \ \hat{i}) + 500(3 \ \hat{i} + 5 \ \hat{j})}{200 + 500}$ $\vec{V}_{cm} = \frac{2000 \ \hat{i} + 1500 \ \hat{i} + 2500 \ \hat{j}}{700}$ $\vec{V}_{cm} = \frac{3500 \ \hat{i} + 2500 \ \hat{j}}{700}$ $\vec{V}_{cm} = 5 \ \hat{i} + \frac{25}{7} \ \hat{j} \ m/s$.

Two particles of masses $200 \ g$ and $500 \ g$ are moving with velocities $10 \ \hat{i} \ m/s$ and $3 \ \hat{i} + 5 \ \hat{j} \ m/s$ respectively. The velocity of the center of mass of the system is:

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