Two objects of masses 200 text{ g} and 500 te | vedclass

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(C) Given: $m_1 = 200 	ext{ g}$,$m_2 = 500 	ext{ g}$.Velocities: $\vec{v}_1 = 10 \hat{i} 	ext{ m/s}$,$\vec{v}_2 = (3 \hat{i} + 5 \hat{j}) 	ext{ m/

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

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(C) Given: $m_1 = 200 	ext{ g}$,$m_2 = 500 	ext{ g}$.Velocities: $\vec{v}_1 = 10 \hat{i} 	ext{ m/s}$,$\vec{v}_2 = (3 \hat{i} + 5 \hat{j}) 	ext{ m/s}$.The velocity of the centre of mass $\vec{v}_{CM}$ is given by the formula:$\vec{v}_{CM} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2}{m_1 + m_2}$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} 	ext{ m/s}$.

Two objects of masses $200 \text{ g}$ and $500 \text{ g}$ possess velocities $10 \hat{i} \text{ m/s}$ and $(3 \hat{i} + 5 \hat{j}) \text{ m/s}$ respectively. The velocity of their centre of mass in $\text{m/s}$ is:

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