### Rigid Body

A billiard ball ( mass $M$, radius $R$) is placed on a table with kinetic friction coefficient $\mu$.
At $t=0$ the ball is struck (for an infinitesimal duration $\Delta t$ such that $F\Delta t$ is nonzero) horizontally by a cue at a height $R$ from the table and start moving in a velocity $v_0$.
1. What is the final speed of the center of mass of the ball?
2. At what height (from the center of mass) one has to strike the ball so that rolling motion starts immediately?