Question

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 los

Answer 1

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?

Answer 2

A good question. I was always wondering how to solve it.

Answer 3

Hold on, let me go to the nearest Pool Bar.

Answer 4

it's freaking hard i think i got the answer

Answer 5

it looks like an n-body problem, with n=10 balls and 4n variables for each ball (x,y position; x,y-velocities).

I don't see how you can find an analytical solution, except by considering piecewise the possible rebounds, collisions and collision tests.
I think you would have to solve this by simulation.

Please do reask this problem to get more answers, but also tell us where it was posed (Physics Olympiad?) and what complexity and method the answer takes, if any. Do you really treat it as a 10-body problem, or use energy or center-of-mass somehow?

>Just to make it clear, a ball is 'potted' if at least half of the ball is in area of the 'pocket'
The potting condition is: (x,y) are within 0.25m (half-diameter) of any of the four pocket centers {(0,0), (0,8), (4,0), (4,8)}
Mind you, just to be pedantic, we can't "remove" a ball as soon as we know it is guaranteed to be potted, as a second ball might be only partially in the pocket and collide with it - so we need both an "in-pocket" and proximity test before we remove a ball.

Answer 6

Exactly, with this problem you need to think like the Mythbusters—simulation style, and put down the pen and paper.

Answer 7

ugh still though :\

Answer 8

what simulation software you can use for this type of questions?

Answer 9

Pool Master Pro. Available on Android.

Answer 10

...I tried! Hehehe.
So, possibly,
a.) 32.5 Degrees angle
b.) The Minimum number of turns could be 7
c.) 4
d.) 32.5 degrees as well, but in 2m, 5m position

Just warning you though, this is, by the laws of Physics, almost inaccurate; I just simulated it without considering Friction and Bounces.