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#1 2007-09-12 09:30:59

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Snooker

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 coordinates:

                                      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'
                                    39vop0ci.jpg

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?

Last edited by Daniel123 (2007-09-12 09:31:54)

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#2 2007-09-12 22:06:45

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Snooker

I think the only realistic way of doing this is to make a computer simulation and try out angles from that. The mathematics of it would get horrific.


Why did the vector cross the road?
It wanted to be normal.

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#3 2007-12-11 18:30:10

Kargoneth
Member
Registered: 2007-08-11
Posts: 33

Re: Snooker

Jeez...

My first thought: That's a huge fricken' table!

My second thought: The possible combinations to try are overwhelming!

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