1. ## Billiards

The Diagram below depicts a Billiard table. It is perfectly smooth ( no friction), the cushions are perfectly elastic so the ball never decelerates. Every bounce is a perfect reflection ( angle of incidence=angle of reflection)

The table is 9 feet wide and 7 feet high and there are only 4 pockets ( one in each corner)

There is a little mouse in the bottom left hand pocket who is fed up with the red ball in it so he hits it really hard so that it rolls out of the pocket at a perfect 45 degree angle to the sides of the table. Will the ball keep rolling for ever or will it land in a pocket....if the latter, which pocket>?

edited as image was too big

2. ## Re: Billiards

I calculate that it will <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">fall in the pocket directly opposite the mouse after going closwise for several turns then counterclockwise for several more</span hide>

Steve

3. ## Re: Billiards

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">It ends up in the upper right pocket.</span hide>

4. ## Re: Billiards

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">top right corner</span hide>

5. ## Re: Billiards

Well Done Ban

I will defer to your answer as the first official correct answer, as it was clear and concise.

<img src=/S/whisper.gif border=0 alt=whisper width=29 height=17> I didn't quite understand Hans's previous diagram as it didn't start off at 45 degrees, but he was correct

6. ## Re: Billiards

My diagram "unfolds" the path of the billiard ball by mirroring the table. The path of the billiard ball becomes a straight line (at 45 degrees!) that ends up in a corner after having traveled 7x9 = 63 feet horizontally and 9x7 = 63 feet vertically.

7. ## Re: Billiards

Thanks Hans for the clarification, I knew you knew, so I shall take the <img src=/S/trophy.gif border=0 alt=trophy width=15 height=15> away from BAN ( sorry BAN) and firmly place it in your hands sir

<img src=/S/whisper.gif border=0 alt=whisper width=29 height=17> I was being a bit mischievous, sorry

8. ## Re: Billiards

You don't need to take away the trophy from BAN - I'm sure he solved it independently.

9. ## Re: Billiards

What was wrong with my answer?

Steve

10. ## Re: Billiards

Sorry Steve

A typical Monday morning. I completely overlooked you answer whilst scrolling down, my apologies you were first and therefore you can have a <img src=/S/trophy.gif border=0 alt=trophy width=15 height=15> and a [bar of chocolate] too as a diplomatic gesture of good will

11. ## Re: Billiards

Mmmm...chocolate.... <img src=/S/heart.gif border=0 alt=heart width=15 height=15>

12. ## Re: Billiards

Lyra

I have been reliably informed .... "Men like chocolate, women NEED it" would that be correct

13. ## Re: Billiards

Thanks. Chocolate is good. <img src=/S/smile.gif border=0 alt=smile width=15 height=15>

Steve

14. ## Re: Billiards

Absolutely, in my (limited) experience Jerry <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

15. ## Re: Billiards

<img src=/S/sad.gif border=0 alt=sad width=15 height=15> That's a bummer, I hadn't won a trophy for quite some time....but at least now I understand the diagram Hans drew <img src=/S/artist.gif border=0 alt=artist width=34 height=29> <img src=/S/clever.gif border=0 alt=clever width=15 height=15>

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