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.
About that, has anyone noticed the test isn't very consistent? In the first exercise the speed of a raptor is 25 m/s, in the second exercise the wounded raptor runs at 10 m/s. So far, so good. But in the third exercise the raptors run at 10 m/s. Why, are they wounded? And of course, can the raptors chew through walls?
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
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
The optimal solution, i.e. the human's trajectory, is a function and therefore has to be found through variational calculus. Not sure there is an analytical one, but the optimum should be quite easy to find numerically.
My guess would be that there is a relatively simple analytical solution iff the raptors are allowed to accelerate infinitely, but the capped speed probably makes it a bit more difficult.
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.
A polite expression of opinion here has been downvoted, and a comment elsewhere that just informs that this question appeared in someone's exam has been upvoted _twice_!
http://www.google.com/search?q=lion+and+man+problem+&ie=...
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http://mathworld.wolfram.com/PursuitCurve.html
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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.