How can you use the law of reflection to model a game of billiards?

Answer 1

You cannot. The rolling of a billiard ball and its reactions to the tabe and other balls is much more complex, as each contact affects not only angle of deflection, but rotational momentum as well. When a ball contacts another ball or a table rail, except for a dead head-on shot, the center of gravity being off center will induce a greater angle that would exist based simply on angle of reflection. In addition, there can be a "crush" on hard impact into a rail that reduces the angle rather than increasing the angle. This is a complex problem in physics and cannot be determined using simple rules for anything other than the simplest of billiard shots.