A regulation billiards table is twice as long as it is wide, has six pockets in the conventional positions, and a total of 18 “rail sights” (the little aiming circles or diamonds along all four sides). Rail sights and pockets form 24 equally spaced divisions around the table. You are at the “head” of the table, and desire to hit the cue ball from against your rail (the head rail), over the “foot spot” (that little dot near the other end), off the far (foot) rail, and back into one of the corner pockets on your end. For non-experts, (including me!), the foot spot is always two rail sight marks from the from the foot rail and centered between the two long sides.
Assume the following:
The ball rolls only – no sliding, no “english”, no leaving the table, therefore all shots go straight since the table is level
Coefficient of friction of the rolling ball on the table is 0.05 (a realistic value)
The ball always makes a perfect collision with the bumper (i.e. no energy loss and no friction while in contact) Ignore the size of the ball and pockets – treat both as point entities.
Mass of the ball = OOOPS!, some pool shark has switched your cue ball for one of unknown weight (mass).
Q1: Where do you place the cue ball in order to make the bank shot?
Q2: What is the minimum initial speed you must give to the ball on this trajectory in order to make the shot (assume that if the ball stops exactly at the pocket, you succeeded)
Puzzle Thoughts
