Description: Mindless Philosopher - Aaron's Sphere of Influence
mindless philosopher blog (1) mindless philosopher (1)
My wife is out of town this weekend, so I decided to stay up late Saturday night and scratch a figurative itch that’s been in the back of my mind for a few years — XKCD’s 3-velociraptor problem. (I spent early Saturday night at an Ira Glass show at Wolf Trap, so apparently I don’t turn into a complete hermit when the mate is away.)
I’m not a mathematician (my brother got those genes), so I reached for my trusty brute-force, computer-simulation experience to solve the problem. At first glance, you’d think that you want to run toward the limping velociraptor at the top. And you’d be right, but to a surprisingly small extent. The optimal angle is about 32 degrees–only two degrees different from the angle you’d run to bisect the vicious predators if all velociraptors were healthy. Of course, there’s a symmetrical solution on the left side
The reason that the answer differs so little in the top-VR-is-injured variation is that over three seconds, the two healthy beasts only reach 12 m/s, which is only 2 m/s faster than the injured animal. I was disappointed when I realized that Randall probably didn’t solve the problem before writing the comic–if he had, I would have expected a more interesting conclusion.