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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: $m_1 = 200 \ g$,$\vec{v}_1 = 10\hat{i} \ m/s$,$m_2 = 500 \ g$,$\vec{v}_2 = 3\hat{i} + 5\hat{j} \ m/s$.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 objects of masses $200 \ g$ and $500 \ g$ have velocities $10\hat{i} \ m/s$ and $3\hat{i} + 5\hat{j} \ m/s$ respectively. The velocity of their center of mass (in $m/s$) is:

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