A cue ball (a uniform solid sphere ofmass m and radius R) is at rest on a levelpool table. The ball is positioned at x = 0. A poolcue is used to give the ball a sharp horizontal hit at itsmidpoint, as is shown in (Figure 1). This results in aninitial translational velocity v0 inthe +x-direction. The coefficient of kinetic friction betweenthe table and the cue ball is ?k. As the ball slidesalong the table, it begins to rotate. Eventually, its angularvelocity increases to the point where the ball rolls withoutslipping. In terms of m,R,?k,v0, and accelerationof gravity g, calculate (a) the translationalacceleration of the cue ball while it is sliding; (b) the angularacceleration of the cue ball while it is sliding; (c) thetranslational and rotational velocities of the cue ball as afunction of time, while it is sliding; (d) the distance the cueball travels before it begins to roll without slipping.

Find the distance that the cue ball travels during thistime.

Express your answer in terms of some or all of thevariables m, R, v0, ?k, and g.

x = 0 -X