Math Is Fun Forum

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Interesting velociraptor problem

From http://xkcd.com/135/

My answer

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Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: Interesting velociraptor problem

Don't you have to take into account the amount of time that the velociraptor will take to devour you? I mean, it won't swallow you whole, the average human being would be too large. Also, environmental conditions and other sorts of things would have to be taken into account. Is it rainy? Is the road bumpy? Easy to trip?

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Interesting velociraptor problem

sadly in this problem the raptor catches you almost just before he reaches top speed.   In fact he'll hit you at precisley (6 + 2 sqrt(89) mps which is about 24.86. Having to use the piecewise function would have been more interesting.  But you're running at 6mps so its equivilent to about a 19 mps impact. He'll probably slide at least another 4-to 5 meters on his face.

I'd like to see someone solve the three sided raptor problem though. THAT thing looks tough.

Last edited by mikau (2007-11-04 07:15:21)

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A logarithm is just a misspelled algorithm.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Interesting velociraptor problem

It might be hard to actually do, but the steps involved aren't too difficult.  It's actually a really nice problem which sums up most of the best results from calculus.

Nothing in the problem states anything about raptors slowing down when they turn, so the equivalent solution is to find where the raptors run the farthest.  So given a 2d vector d, the direction you run in, we can calculate vector paths for each of the raptors, which will represent not only direction, but speed (magnitude) as well.  What we need to find is when the two intersect which can be done various ways.  If the curve is simple enough, algebra solutions are possible.  Otherwise, approximation isn't too hard to do.  Now we have the point where the raptor gets to you, so we also have the point in time (that's what our functions are based off of, and our running path is linear).  So now we can calculate the arc length of the path the raptor ran.  Now this is the value we want to maximize, so we differentiate it with respect to our running direction.  Find the max for this, and we're done.

Thinking about it some more, each of those steps would have to be approximated.  So what you're going to end up with is a really big algorithm that runs for quite a while, but in the end a solution is possible.  I'm pretty certain the solution will be almost straight up.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."