Water!
Labels: mathschallenge
posted by Ragknot at
7:37 PM
Saturday, October 31, 2009
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13 Comments:
this is a VERY old question being repeated, just browse through the older questions, and you will find it. I remember the situation and the graph.
S:
The gratification of solving a problem on your own is worthwhile.
Copying the solution from someone else might make someone else think you're smart, but if the only reward is self gratification, then why bother?
Hi Ragknot and S. Numerically I get the nearest point is at (6.11,15.265) and is 14.762 miles away. Those numbers are rough and ready and were found by plotting graphs.
Is there an "elegant" (i.e. not requiring numerical methods) solution to this problem?
Slight improvement in the numbers.
Nearest point is (6.10963,15.2646) and is 14.7623 miles away.
Great to hear from you Chris.
I don't know an "elegant" solution. I know there's two solutions that are almost the same distance but not at the same angle.
But I had wondered how accurate could a man on a camel be? My idea was to say "Go due south".
Chris,
That is about what I got
x= 6.10963251010011
y= 15.2645590492447
dist =14.7623160202005
There's another solution less than 15 miles. The minimum distance in this area is
x=20.5753561000001
y=23.7897165599637
dist=14.9284263620584
Ragknot, there is no gratification in solving the same question twice.
If you post the same question from old days, it means that you are quite new here.
Anonymous. Why do you bother to complain - why not just let it pass? I haven't seen the problem before because I've only been visiting for 6 months tops. I'd rather have a repeat problem than none at all.
Chris,
Elegant solution should be to find x and y by finding zero(s) of the derivative of the distance function.
i.e. find x for
d/dx [sqrt[(30-y)^2+(7-x)^2]]=0
OR
d/dx[sqrt[(30-10sin(x/10)-10cos(x/5)+x)^2+(7-x)^2)]]=0
find x where dD/x=0 to find min point of the distance function. substitute x into y function to find y....voila.
But if your calculus is a rusty as mine, using the plot and graph sounds a lot more attractive.
Cam
According to HowStuffWorks, camels can travel fine without water for about 5 days during the height of summer. They can travel about 25 - 30 miles per day.
Therefore he should sacrifice himself and let his camel continue on its journey knowing that it will survive both there and back.
Hi Cam. My calculus is surprisingly good (it was good enough to solve the wonderul "Bug on a rubber band" problem). I found the derivative of the distance function easiliy enough. But it needs numerical methods to solve. So I did it by graphing (using Mathematica) and using trial and error to find the minimum distance (the variable was the radius of the circle centred on (7,30)).
The second result was obtained by numerically finding the zero (near x=6) of the derivative of the distance function, but using numerical methods (no sweat for Mathematica).
I was hoping that there was a solution that didn't require numerical methods.
s:
I don't post for my own gratification. I try to present something that someone else can enjoy figuring out. After several days with little food for thought being submitted, I wanted to fee the hungry. (I was getting very hungry, but my post did little for me.) Sometimes all you can find is leftovers, which I served for newbies.
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