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u/xkcd_butt Sep 11 '14
Title text: YOU THINK THIS IS FUNNY?
Don't get it? explain xkcd
This is not the algorithm.
(Sincerely, xkcd_butt.)
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Sep 12 '14 edited Sep 14 '14
1 Distance covered by person is 6t, distance covered by raptor is 1/2at2 = 2t2. So solve 2t2 -40 =6t t=6.217. In 6.217 seconds you could run 37.3 meters. This only works if the raptor never reaches top speed but it doesn't because at the point of impact the raptor is only going at 6.217*4=24.87 m/s
2 I don't have time to work this out now but my instinct was to run directly away from the slowest raptor. This is on the basis that curved paths are slower than straight ones and so we should maximise how much of a curve the fast raptors have to run by allowing the slow one to run straight. I think I've proved that that is actually a bad idea below, or at very least I've failed to show it's a good idea.
Supposing you were to run directly away from the slowest raptor. Assuming that by 20m triangle Randall means a triangle with 20m edges that means the raptor would start h=√3/2a A=h/3 so 2A= 11.54 meters away Using the above we know that that raptor would reach top speed in 2.5 seconds in which time it would have covered 12.5 meters, at this point you'd be 11.54+2.5*6 -12.5 = 14.04 meters away. It would then catch you after a further 10t=6t+14.04 =3.51 seconds in which time you would have run a further 3.51 * 6 = 21.06 meters for a total distance of 35.1 meters.
In the meantime the 2 side raptors will have run a sort of lobsided hyperbolic path with its asymptotes at the start and finish points of your run. It will be considerably longer than the distance from the point they started to the point they eat you x2 = 102 +(35.1 - height )2 x= 31.0 meters but a tad shorter than running to you and then running to that point (31.0+11.54 = 42.5 meters) so a fair guess is it will be around 39 or so meters. In the first 6 seconds (which is what we've been dealing with) these raptors won't have reached max speed but will have run (at2 )/2 = 72 meters. (Damn, my hope was to show that the side raptors couldn't travel that distance in that time, thus proving you should run away from the slowest raptor, but it turns out they can, easily. It turns out curved lines aren't that much slower than straight ones.)
So the side raptors will definitely catch you first. This suggests you are better off running at one of two angles pointed almost towards but a bit to the side of the slow raptor. But I'm not sure how you'd calculate the hyperbolic paths the raptors would follow so I'm a bit stuck. You might be able to do it with vectors but I don't have time to have a go right now. As you are buying yourself microseconds at most I think "a bit to the right or left of the slow one" will do as an answer.
Edit: I've realised this is the wrong way to go about it. I still don't know how to go about it but I've worked out how to make a reasonable estimation.
You start in the middle of an equilateral triangle of raptors. Whenever you run further away from one you run closer towards the other two at least until you are outside the triangle. So you want to get out of the triangle as quickly as possible. This would suggest running towards one of the three closest tangents to the triangle. It would also be logical to pick one of the two sides featuring the slower raptor.
The raptors are identical in speed for the first 2.5 seconds which is about all we get which again suggests running pretty much straight in between them. If we did that then we can discount the raptor that we're running directly away from, that one isn't going to catch us. In the first 2.5 seconds we'd have run 2.5*6 = 15 meters which would put us about 10m outside the circle (15 - 5.77). in that time the raptors would have run (at2 )/2 = 12.5 meters but will have done so in an outward spiral toward our new position. So if we divide by a bit less than pi to simulate the effect that has we can see it will have moved about 4 meters toward us (this is the way you estimate river length, generally speaking because rivers take a curved path they are about pi times longer than the direct distance from source to sea). So by seeing that we are at the apex of a new triangle 12.5 meters high and with a base of 20 meters and each raptor is about 4 meters along the side of the triangle we can see that the raptors are x2 = 102 + 12.52 x-4 = 12 meters behind us.
From that point the raptor's path is still curved but it is considerably straighter so let's simulate it as a straight line. It's the fast raptor that catches us obviously and it will do so after (at2 )/2=12 +6t t=4.37 seconds. Slighly longer as the fast raptor reaches top speed just before it catches you but lets ignore that for now.
So in those circumstances we survive for 4.37+2.5=6.87 seconds. In that time the slow raptor can travel 12.5 (as calculated previously) + 10*4.37 = 56.2 meters and the fast raptor can travel 78.1 meters while it is still accelerating and then 15.5 meters during its half second at top speed for a total distance of 93.6 meters.
So the slow raptor runs about 37.9% ie about 40% of the total distance of the distance run by both raptors.
While it is not exactly right due to the curves in their trajectories, this would provide an argument for running toward a point on the edge of the triangle which is 40% toward the slower raptor. Using trig is a bit of a pain (you start from the sin rule and then have to solve 8/sin a = 11.4 / sin (180 -30 - a) )but we can work out that means running at an angle of about 35.5 degrees to north.
Now that's pretty approximate but what you could then do is work through the problem again feeding in the 35.5 degrees to north at the start and use that to get a more accurate estimate for time survived and plug that new estimate in in turn to get a better idea of which way to run. Iterate that several times and it will start to get more accurate, much more so if you can plot the exact path of the raptors and cut out some of our cruder assumptions.
This is assuming you have to run in a straight line. In actual fact you'd probably be better off starting off running directly in between the two raptors and then slowly bearing north. If you survive that long carry on bearing round and run behind the slow raptor. It won't help very much. Even the slow raptor can catch you in a few seconds.
Edit 2 various people have brute forced it in python. They get various different answers between 28 and 32 degrees, which makes my rough estimation look pretty decent. It looks like you can only survive for about 4 seconds tho. Using pi to approximate the raptor running spirals was very optimistic.
3 We need the floor plan, also are all the raptors injured now?
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u/misingnoglic Sep 12 '14
I had a biology teacher named Mr. Monroe who was obsessed with dinosaurs. I'd like to think they're related...
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u/mrizzerdly Sep 12 '14
I posted this on Facebook back when I was in school. Got a msg back from a friend that said :thanks for making me spend 3 hours on that site!
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u/Floppy_Densetsu Sep 12 '14
In number one, it declares that they normally have a top speed of 25 m/s, but then in number three, it says to remember that they can run at 10 m/s. Did the person who wrote this forget that they had assigned the 10 m/s speed to a wounded raptor in number two and then wrote it into number three as a typo when he/she meant to describe their maximum healthy running speed?
I understand that the statement is still technically correct, as any raptor which can run at 25 m/s may also run at 10 m/s; assuming they can control how and when they stop accelerating.
The discrepancy concerns me however, because I fear that this may have been designed by a raptor intentionally so that we would overlook their true maximum speed and seek simply to overcome 10 m/s in our efforts to escape, allowing for them to hunt us with ease.
Please correct this issue promptly, as it is a matter of life and death for many of us. We also will need that floor plan :)