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 balls (each with a diameter of 0.25m) placed at the following coords:
2m,1m…(white ball)
…and red balls…
1m,5m… 2m,5m… 3m,5m
1m,6m… 2m,6m… 3m,6m
1m,7m… 2m,7m… 3m,7m
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 balls 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 balls are potted the quickest?
b: What is the minimum amount of contacts the balls 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?