My math teacher gave me this problem ITS ******* IMPOSSIBLE!!?

[The question was asked once previously and got no answers]

Let's start by agreeing terminology

- units are in meters. Pick Origin as top left (y axis increases downwards; not sure if choosing x=0 down the middle of the table helps.)

- refer to the coordinates of each ball's centroid

- link to picture is below

Label the balls and initial coordinates:

white ball W @ (2,1) and red balls

A (1,5) B (2,5) C (3,5)

D (1,6) E(2,6) F(3,6)

G (1,7) H(2,7) I(3,7)

and the test for whether a ball's center is inside a pocket is:

P1: x+y ≤ 1/2√2 ≈ 0.3536

P2: (4-x)+y ≤ 1/2√2

P3: x+(8-y) ≤ 1/2√2

P4: (4-x)+(8-y) ≤ 1/2√2

Now let's discuss strategies for potting balls.

If a ball is hit, its trajectory is changed and one of 3 things eventually happens as a result:

i) it gets pocketed without any further collisions, maybe with some bounces (off cushion)

ii) it falls into a steady-state where its trajectory bounces off cushion but is never pocketed.

iii) it eventually collides with another ball, at which time we need to recompute trajectories. We need a collision test for trajectories.

(A collision test for coordinates of two balls P,Q is simply that their centroids are ≤ 0.5m apart.)

We want an algebraic way to codify all that as simply as possible, for all 10 balls.

I would derive a subresult that if we know a ball's position and velocity (vx(t),vy(t)), and if we are given that it does not have further collisions, we can determine if its trajectory will cause it to be pocketed or steady-state. Working backwards, we can determine the range of angles of contact require by the ball that strikes it to ensure it is pocketed.

[WILL CONTINUE]

I'm in Pre-calculus at a tuition.... now we have 30-50 issues every week on-line, and the occasional at school quiz that's frequently just one main issue. I needed to drop calculus final semester seeing that he gave strategy to so much homework for my style. A "W" to your transcript won't harm your probabilities of having permitted, so long as you've gotten a well reason behind it... or for those who re-take the category and get an A or B in it you will have to be best!

First check the equivalent...then check the value...by mixed and crossed with the coordinat..x..y..z..then...check the opponent...with the mirror...ratio the diameter of the reds ball...so you have to know who the red ball that come in to the hole...

b

....

Thats one evil teacher...