Two bodies of mass 4 ,kg and 5 ,kg are moving | vedclass

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(A) The velocity of the centre of mass is given by the formula:$v_{CM} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2}{m_1 + m_2}$Given: $m_1 = 4 \,kg$,$m_2 =

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$\frac{25}{9} \,m/s$

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(A) The velocity of the centre of mass is given by the formula:$v_{CM} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2}{m_1 + m_2}$Given: $m_1 = 4 \,kg$,$m_2 = 5 \,kg$. The velocity $\vec{v}_1$ is along the east (x-axis) and $\vec{v}_2$ is along the north (y-axis).So,$\vec{v}_1 = 5 \hat{i} \,m/s$ and $\vec{v}_2 = 3 \hat{j} \,m/s$.Substituting the values:$\vec{v}_{CM} = \frac{4(5 \hat{i}) + 5(3 \hat{j})}{4 + 5}$$\vec{v}_{CM} = \frac{20 \hat{i} + 15 \hat{j}}{9} = \frac{20}{9} \hat{i} + \frac{15}{9} \hat{j} \,m/s$The magnitude of the velocity is:$|v_{CM}| = \sqrt{(\frac{20}{9})^2 + (\frac{15}{9})^2}$$|v_{CM}| = \sqrt{\frac{400 + 225}{81}} = \sqrt{\frac{625}{81}}$$|v_{CM}| = \frac{25}{9} \,m/s$

Two bodies of mass $4 \,kg$ and $5 \,kg$ are moving along east and north directions with velocities $5 \,m/s$ and $3 \,m/s$ respectively. The magnitude of the velocity of the centre of mass of the system is:

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