A body of mass 2 , kg is moving with velocity | vedclass

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(D) Let the mass of each body be $m = 2 \, kg$ and the velocity be $v = 10 \, m/s$.Initial momentum of the first body: $\vec{P}_1 = mv \hat{i} = 2 	i

Vedclass · Accepted Answer

$5\sqrt{2} \, m/s$

Vedclass · Answer

(D) Let the mass of each body be $m = 2 \, kg$ and the velocity be $v = 10 \, m/s$.Initial momentum of the first body: $\vec{P}_1 = mv \hat{i} = 2 	imes 10 \hat{i} = 20 \hat{i} \, kg \cdot m/s$.Initial momentum of the second body: $\vec{P}_2 = mv \hat{j} = 2 	imes 10 \hat{j} = 20 \hat{j} \, kg \cdot m/s$.Total initial momentum: $\vec{P}_{total} = \vec{P}_1 + \vec{P}_2 = 20 \hat{i} + 20 \hat{j}$.Magnitude of total initial momentum: $|\vec{P}_{total}| = \sqrt{20^2 + 20^2} = 20\sqrt{2} \, kg \cdot m/s$.After collision,the bodies coalesce into a single mass $M = m + m = 4 \, kg$.Let the final velocity be $V$. By the law of conservation of momentum: $\vec{P}_{final} = \vec{P}_{total}$.$MV = |\vec{P}_{total}| \implies 4V = 20\sqrt{2}$.$V = \frac{20\sqrt{2}}{4} = 5\sqrt{2} \, m/s$.

$A$ body of mass $2 \, kg$ is moving with velocity $10 \, m/s$ towards the east. Another body of the same mass and same velocity moving towards the north collides with the former,coalesces,and moves towards the north-east. What is its final velocity?

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