Three particles of masses 10 g, 20 g and 40 | vedclass

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(D) According to the law of conservation of linear momentum,the total momentum of the system remains constant in the absence of external forces.Initia

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$1 \hat{i} + 3 \hat{j} + 10 \hat{k} \ m/s$

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(D) According to the law of conservation of linear momentum,the total momentum of the system remains constant in the absence of external forces.Initial momentum: $\vec{P}_i = m_1 \vec{u}_1 + m_2 \vec{u}_2 + m_3 \vec{u}_3$$\vec{P}_i = 10(10 \hat{i}) + 20(10 \hat{j}) + 40(10 \hat{k}) = 100 \hat{i} + 200 \hat{j} + 400 \hat{k} \ (g \cdot m/s)$Final momentum: $\vec{P}_f = m_1 \vec{v}_1 + m_2 \vec{v}_2 + m_3 \vec{v}_3$Given $\vec{v}_1 = 0$ and $\vec{v}_2 = (3 \hat{i} + 4 \hat{j}) \ m/s$:$\vec{P}_f = 10(0) + 20(3 \hat{i} + 4 \hat{j}) + 40 \vec{v}_3 = 60 \hat{i} + 80 \hat{j} + 40 \vec{v}_3$Equating $\vec{P}_i = \vec{P}_f$:$100 \hat{i} + 200 \hat{j} + 400 \hat{k} = 60 \hat{i} + 80 \hat{j} + 40 \vec{v}_3$$40 \vec{v}_3 = (100 - 60) \hat{i} + (200 - 80) \hat{j} + 400 \hat{k}$$40 \vec{v}_3 = 40 \hat{i} + 120 \hat{j} + 400 \hat{k}$$\vec{v}_3 = 1 \hat{i} + 3 \hat{j} + 10 \hat{k} \ m/s$

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