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Question

From momentum conservation

$\overrightarrow{ P }_{ i }=\overrightarrow{ P }_{ f }$

$m ( ui )+3 m ( D )= mvj +3 m \overline{ v }_{2}$

$mui - m

Vedclass · Accepted Answer

$v=\frac{u}{\sqrt{2}}$

Vedclass · Answer

From momentum conservation

$\overrightarrow{ P }_{ i }=\overrightarrow{ P }_{ f }$

$m ( ui )+3 m ( D )= mvj +3 m \overline{ v }_{2}$

$mui - mvj =3 m \overline{ v }_{1}$

$\bar{v}_{1}=\frac{u i-v j}{3}$

or $\left| v _{1}\right|=\frac{\sqrt{ u ^{2}+ v ^{2}}}{3}$

or $v_{1}^{2}=\frac{u^{2}+v^{2}}{9} \ldots .(1)$

As collision is perfectely elastic hence

$k_{i}=k_{j}$

$\frac{1}{2} m u^{2}+\frac{1}{2} 3 m 0^{2}=\frac{1}{2} m v^{2}+\frac{1}{2} 3 m v_{1}^{2}$

$\Rightarrow u ^{2}= v ^{2}+3 v _{1}^{2}$

$u ^{2}= v ^{2}+3 \frac{\left( u ^{2}+ v ^{2}\right)}{9}$

$\Rightarrow 3 u ^{2}=3 v ^{2}+ u ^{2}+ v ^{2}$

$\Rightarrow 2 u ^{2}=4 v ^{2}$

$v =\frac{ u }{\sqrt{2}}$

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