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I need help with this Math Problem.

#1 blacklce Posted 13 February 2005 - 06:09 PM

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A long rope is pulled out between two opposite shores of a lake. It's pulled so tight that it's perfectly straight.
Because the earth is spherical most of the rope is under water.
The length of the portion of rope that is under water is 70 km long.
How many meters below the surface is the rope at it's deepest point?
The earths radius is assumed to be 6370 km.
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#2 admin Posted 13 February 2005 - 07:28 PM

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Sorry, we don't help with homework.
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#3 blacklce Posted 13 February 2005 - 07:45 PM

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Heh, it's not homework. I can show you the puzzle I'm doing if you don't believe me. It's on the Internet. It's quite fun. I'm on Stage 7 of the Math Section.
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#4 ditto Posted 13 February 2005 - 08:35 PM

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i got 6369.628km
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#5 blacklce Posted 13 February 2005 - 08:44 PM

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#6 mpfeif101 Posted 13 February 2005 - 09:56 PM

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Not that difficult of a problem.

You have a circle with a radius of 6370.
You have a chord with the distance of 70.
You have to find the distance from the middle of the chord to the perimeter. Draw it out, it makes it easier.

Gotta research the theorums and postulates of geometry, I've long forgotten those
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#7 ditto Posted 13 February 2005 - 10:01 PM

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sorry i was in radian mode and forgot to subtract r

.0932km

here's my work

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#8 blacklce Posted 13 February 2005 - 10:14 PM

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Hmmm, that didn't work either.
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#9 blacklce Posted 13 February 2005 - 10:21 PM

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You guys should check this puzzle out, it's quite fun. I'm done the picture and the code part. If anybody needs help, just say so:

http://www.etienne.nu/imagepuz/
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#10 mpfeif101 Posted 13 February 2005 - 10:26 PM

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I'm stuck on the 3rd part of the image puzzle

Maybe I'm just too tired
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#11 blacklce Posted 13 February 2005 - 10:34 PM

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Those crazy magic eyes are kind of hard. Hint: It's one letter.
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#12 admin Posted 16 February 2005 - 01:32 AM

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bigger hint: Oh

It doesn't get any easier, but a photoediting program helps.
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#13 FilmAtEleven Posted 17 February 2005 - 03:37 PM

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I know I'm a week late, but did you solve the math problem already? Shouldn't the answer be .0962 meters?

The distance from the center of the earth to any point on the surface has to be constant at 6370m, meaning the distance to either endpoint of the rope as well as to the point that bisects the arc above the rope are all 6370m. Assuming this, it's just a matter of the pythagorean theorem and some subtraction, right?

Bisecting the rope creates a right triangle with the following dimesnions:

Side (a) = 35 m
Remaining side (b) = the distance from center of earth to rope.

sqrt(b) = 6370*6370 - 35*35

b = 6369.903845

radius of earth (6370) - length of side b (6369.903845) = .096155 meters
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