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I need help with this Math Problem.


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#1
blacklce

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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

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Sorry, we don't help with homework. :tazz:
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#3
blacklce

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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

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i got 6369.628km
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#5
blacklce

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Nope, that answer is wrong.
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#6
mpfeif101

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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 :tazz:
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#7
ditto

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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

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Hmmm, that didn't work either.
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#9
blacklce

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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

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

Maybe I'm just too tired :tazz:
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#11
blacklce

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Those crazy magic eyes are kind of hard. Hint: It's one letter.
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#12
admin

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bigger hint: Oh

It doesn't get any easier, but a photoediting program helps. :tazz:
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#13
FilmAtEleven

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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:

Hypotenuse © = 6370 m
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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#14
Koretek

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thats exactly what I got after I read your answer "Film"
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