In a game of billiards, ball A is given an initial

Chapter 14, Problem 14.51

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QUESTION:

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 \(C^{\prime}\), respectively, and ball B is observed to hit the side obliquely at \(B^{\prime}\). Knowing that \(v_0=4\mathrm{\ m}/\mathrm{s}\), \(v_A=1.92\mathrm{\ m}/\mathrm{s}\), and a = 1.65 m, determine (a) the velocities \(\mathbf{v}_{B}\) and \(\mathbf{v}_{C}\) of balls B and C, (b) the point \(C^{\prime}\) where ball C hits the side of the table. Assume frictionless surfaces and perfectly elastic impacts (i.e., conservation of energy).

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QUESTION:

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 \(C^{\prime}\), respectively, and ball B is observed to hit the side obliquely at \(B^{\prime}\). Knowing that \(v_0=4\mathrm{\ m}/\mathrm{s}\), \(v_A=1.92\mathrm{\ m}/\mathrm{s}\), and a = 1.65 m, determine (a) the velocities \(\mathbf{v}_{B}\) and \(\mathbf{v}_{C}\) of balls B and C, (b) the point \(C^{\prime}\) where ball C hits the side of the table. Assume frictionless surfaces and perfectly elastic impacts (i.e., conservation of energy).

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