Solving xkcd's raptor problem

This looks like a variant of the "Lion and Man" problem which is also described as a "bounded pursuit" problem in the operations research journals:

http://www.google.com/search?q=lion+and+man+problem+&ie=...

-and-

http://mathworld.wolfram.com/PursuitCurve.html

-and-

http://books.google.com/books?id=HeESjfM2geUC (good!)

This problem may have had relevance in World War II all the way to the present: dogfights between airplanes, battleships trying to sink each other, etc.

I've created a quick graph [1] of the survival time running in a single fixed direction. While this doesn't take acceleration into account, the results agree with the article and common sense. No matter which direction you run, one of the 25 m/s raptors will catch you, so your best bet is to run directly toward the weakened one. The code's available here: http://gist.github.com/418783

[1] http://chart.apis.google.com/chart?cht=s&chd=t:0.0,1.111...

What about problem #3 of http://xkcd.com/135/ ? Will xkcd ever publish the floor plan from the next page where you escape from the raptors?

Interesting. Haven't had time to fully create my own solution; I'll have to work on it tonight. If anyone wants what I've got so far (ruby): http://codepad.org/qggAcIKy

An analytical solution would be nice in addition to the simulation one. Even better if the number of sides of the polygon could be parametrized :)

Apparently, from the plot seems that if you are faster than the slow raptor, your best direction is not straight at it, but nearby. This makes some sense because if you you are close to the slow one and far of the fast ones you can outrun go around the slow one.

i had to take an intro calc class recently, my professor put this problem on the final exam.

Why use we instead of I? There is just one author and the we convention used for papers with multiple authors is inappropriate and misleading.

Just a small quibble... the article was otherwise fine if you like that sort of thing.