(Solved): In a game of billiards, ball \( A \) is given an initial velocity \( \mathbf{v}_{0} \) along the l ...

In a game of billiards, ball \( A \) is given an initial velocity \( \mathbf{v}_{0} \) along the longitudinal axis of the table. It hits ball \( B \) and then ball \( C \), which are both at rest. Balls \( A \) and \( C \) are observed to hit the sides of the table squarely at \( A^{\prime} \) and \( C^{\prime} \), respectivelv. and ball \( B \) is observed to hit the side obliquely at \( B^{\prime} \). \( v_{0}=5 \mathrm{~m} / \mathrm{s}, v_{C}=3.2 \mathrm{~m} / \mathrm{s} \), and \( c=1.22 \mathrm{~m} \). Determine \( (a) \) the velocities \( \mathbf{v}_{A} \) and \( \mathbf{v}_{B} \) of balls \( A \) and \( B,(b) \) the point \( A^{\prime} \) where ball \( A \) hits the side of the table.