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#1 2007-09-13 07:30:59

Daniel123
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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'
                                    http://www.mypicshare.com/thumbs/20070912/39vop0ci.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 (2007-09-13 07:31:54)

 

#2 2007-09-13 20:06:45

mathsyperson
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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.
 

#3 2007-12-12 17:30:10

Kargoneth
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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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