My homework

[BrotherTi]

This isn't really my homework but I do want to see who can solve it. It's actually pretty hard.

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?

stable2.jpg

~BrotherTi

[Dragonman855]

Re: My homework

My brain hurts.

[wtholyf]

Re: My homework

No offense, but this is a dumb question.

You state "The white ball is then shot at a particular angle from 0 to 360 degrees (0 being north, and going clockwise.)"

This implies that the ball is shot at random. Normally, this wouldn't be an issue; however, your first quesiton is "What exact angle/s should you choose to ensure that all the balls are potted the quickest?"

I didn't realize I could choose...

Next, your question fails to specify how much force is being put into the white ball. This is important because assuming that each shot has the same amount of force is ambigous. I could argue I hit the ball either directly down or up, so it causes the table to break thus causing all the balls to fall into a corner pocket without touching the white ball at all. It would also leave the white ball "last."

You also exemplified the ball losing no energy by stating "i.e. no loss of energy via friction, air resistance or collisions." Am I to assume the ball loses no velocity, force, or acceleration upon hitting a ball? If that were Indeed the case then hitting the ball at either 67.5 or 292.5 degrees would be the "quickest" way to put them all.

In order to make this a valid question, you must give enough information for us to at least be able to identify the force being put into the ball, it's weight, and the weight of the other's balls. After that you must revise your question so it is free of all errors pointed out.

If you are not looking for a numerical answer, then you must specify how much energy is forced onto the white ball.

Other than all that; this really is a stupid question...