Chapter 10, Problem 99GP

If a billiard ball is hit in just the right way by a cue stick, the ball will roll without slipping immediately after losing contact with the stick. Consider a billiard ball (radius r, mass M) at rest on a horizontal pool table. A cue stick exerts a constant horizontal force F on the ball for a time t at a point that is a height h above the table’s surface (see Fig. 10–68). Assume that the coefficient of kinetic friction between the ball and table is ${\mu }_{\text{k}}$. Determine the value for h so that the ball will roll without slipping immediately after losing contact with the stick.