Question 103 of 130

A ball with a speed of $9m{s}^{-1}$ collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of $30^{\circ}$ with the original direction. If the ratio of velocities of the balls after the collision is $x:y$, then what is the value of $x$?

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Answer: 1

From conservation of momentum along $y-$axis.
${\vec{P}}_{iy}={\vec{P}}_{fy}$
$0+0=m{v}_{1}\sin 30^{\circ}\hat{j}+m{v}_{2}\sin 30^{\circ}\left(-\hat{j}\right)$
$m{v}_{2}sin30^{\circ}=m{v}_{1}sin30^{\circ}$
${v}_{2}={v}_{1}$ or $\dfrac{{v}_{1}}{{v}_{2}}=1$