A 'snooker' table (measuring 8 metres by 4m) with 4 'pockets' (measuring 0.5m and placed at diagonal slants in all 4 corners) contains 10 b***s (each with a diameter of 0.25m) placed at the following coords:2m,1m...(white ball)
The white ball is then shot at a particular angle from 0 to 360 degrees (0 being north, and going clockwise).
Just to make it clear, a ball is 'potted' if at least half of the ball is in area of the 'pocket'
Assuming the b***s travel indefinitely (i.e. no loss of energy via friction, air resistance or collisions), answer the following:
a: What exact angle/s should you choose to ensure that all the b***s are potted the quickest?
b: What is the minimum amount of contacts the b***s can make with each other before they are all knocked in?
c: Same as b, except that each ball - just before it is knocked in - must not have hit the white ball on its previous contact (must be a red instead of course).
d: What proportion of angles will leave the white ball the last on the table to be potted?