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 the figure).(Figure 1) Assume that the coefficient of kinetic friction between the ball and table is μk.
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Determine the value for h so that the ball will roll without slipping immediately after losing contact with the stick.
Express your answer in terms of the variables r M, F, μk, and appropriate constants.