An important problem in billiards or pool is the determination of the height at which you...

An important problem in billiards or pool is the determination of the height at which you should hit the cue ball to give it backspin, topspin, or no spin. With this in mind, at what height h should the cue hit the ball so that the ball always rolls without slip, regardless of how hard the ball is hit and how much friction is available? Assume a uniform ball of mass m and radius r. You can determine this position without having to worry about the impact between the cue and the ball by studying an arbitrary horizontal force applied to a ball at height h.

Figure P7.55