A body of mass m moving with velocity v colli | vedclass

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(C) Let the initial velocity of the first body be $\vec{u}_1 = v\hat{i}$ and the second body be $\vec{u}_2 = 0$.After the collision,the velocity of th

Vedclass · Accepted Answer

$\frac{2}{\sqrt{3}}v$

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(C) Let the initial velocity of the first body be $\vec{u}_1 = v\hat{i}$ and the second body be $\vec{u}_2 = 0$.After the collision,the velocity of the first body is $\vec{v}_1 = \frac{v}{\sqrt{3}}\hat{j}$.Let the velocity of the second body be $\vec{v}_2 = v_{2x}\hat{i} + v_{2y}\hat{j}$.By the law of conservation of linear momentum:Along the $x$-axis: $mv = mv_{2x} \implies v_{2x} = v$.Along the $y$-axis: $0 = m(\frac{v}{\sqrt{3}}) + mv_{2y} \implies v_{2y} = -\frac{v}{\sqrt{3}}$.The magnitude of the velocity of the second body is $v_2 = \sqrt{v_{2x}^2 + v_{2y}^2} = \sqrt{v^2 + (-\frac{v}{\sqrt{3}})^2} = \sqrt{v^2 + \frac{v^2}{3}} = \sqrt{\frac{4v^2}{3}} = \frac{2}{\sqrt{3}}v$.

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