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# Interesting one - A Cat and A mouse

Best Answer EventHorizon, 05 July 2012 - 02:30 AM

(Hint: don't look for the curve, just examine the distance between them and how it changes with time)

Spoiler for Answer for the speed of the cat

I'll try (again) to find the equation for the path in a bit.
Edit: I thought I'd include the last equation I got, but kept failing to verify. So I don't know it if is correct.
Spoiler for Maybe the path?
Go to the full post

20 replies to this topic

### #11 Yoruichi-san

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Posted 03 July 2012 - 11:06 PM

Spoiler for The maths

Oops, making a correction. I want the x-component, not the y-component. Also, I realized this whole thing might be easier if I put in terms of theta(t), instead of X(t). Will try when I have time.
• 0
Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.

### #12 mewminator

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Posted 04 July 2012 - 08:35 AM

Maybe
Spoiler for Possibly

Edited by mewminator, 04 July 2012 - 08:37 AM.

• 0

### #13 fabpig

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Posted 04 July 2012 - 03:28 PM

Spoiler for Further to my above (with just a little maths)

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You must not think me necessarily foolish because I am facetious,  nor will I consider you necessarily wise because you are grave.  Sydney Smith.

### #14 EventHorizon

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Posted 05 July 2012 - 02:30 AM   Best Answer

(Hint: don't look for the curve, just examine the distance between them and how it changes with time)
Spoiler for Answer for the speed of the cat

I'll try (again) to find the equation for the path in a bit.
Edit: I thought I'd include the last equation I got, but kept failing to verify. So I don't know it if is correct.
Spoiler for Maybe the path?

• 0

### #15 bonanova

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Posted 05 July 2012 - 05:55 AM

Spoiler for my method

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Vidi vici veni.

### #16 EventHorizon

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Posted 05 July 2012 - 09:05 PM

Spoiler for Maybe the path?

I found a mistake in the derivation, so my equation is wrong. I accidently omitted something which made it much easier to solve, but incorrect.
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### #17 Yoruichi-san

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Posted 05 July 2012 - 09:49 PM

Spoiler for The maths

Further correction. Somehow I always inadvertently put a - instead of a +...

Haven't had a chance to further work on a solution, though. I'm thinking u-sub or trial and error (guess the general form of the solution and then solve for constants).
• 0
Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page! Episode 3 is finally here!

When life hands me lemons, I make invisible ink.

### #18 EventHorizon

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Posted 06 July 2012 - 08:03 AM

Spoiler for Path of the Golden Cat (that sounds like a book/movie title...)

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### #19 fabpig

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Posted 06 July 2012 - 10:14 AM

Spoiler for A bit more..

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You must not think me necessarily foolish because I am facetious,  nor will I consider you necessarily wise because you are grave.  Sydney Smith.

### #20 bonanova

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Posted 06 July 2012 - 10:49 AM

Spoiler for Path of the Golden Cat (that sounds like a book/movie title...)

That seems to tie a bow on it.

Below is a plot of
B my catenary equation
C your final equation quoted above [plotted vs 1-x to make curves congruent]
D my simulation of a thousand points using n = 1.618033989 to make cat and mouse arrive at [1,1] simultaneously.

The light blue arrow is the mouse's path, at unit speed.

C and D are indistinguishable, lending credence to both and casting doubt on the catenary hypothesis.

• 0

Vidi vici veni.

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