Maximizing Distance and Angular Velocity: Solving a Billiard Ball Problem

[Nanoath]

Homework Statement

A billiard ball is struck by a cue as is shown in the figure. The line of action of the applied impulse is horizontal and passes through the center of the ball. The initial velocity v0 of the ball after impact, its radius R, its mass m, the acceleration due to gravity g, and the coefficient of kinetic friction µk between the ball and the table are all known.
a) How far will the ball move before it ceases to slip on the table and starts to roll?
b) What will its angular velocity be at this point?

Homework Equations

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The Attempt at a Solution

I need help getting started, this problem is driving me nuts.
We are looking for distance X between the points where the ball is not rotating and where it starts to rotate due to friction force. If I'm correct, initially the angular velocity is 0, but at the point where it starts moving it becomes greater than 0. The velocity of the ball is highest at V0.
meeh... I'm not sure how to prove that with calculus -_-

 

[Doc Al]

Apply Newton's 2nd law to both translational and rotational motion of the ball due to the friction force. Hint: The angular speed increases as translational speed decreases. Solve for the point where it rolls without slipping. (What's the condition for rolling without slipping?)

 

[Nanoath]

Thanks, trying it out now :D