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10/17/2009 06:34:59 PM · #1
Here is the question for people who enjoy science and understand geometry as well:

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 77 degrees

What is the circumference
10/17/2009 06:46:16 PM · #2
is this even possible? Wouldn't you have to know the degree per kilometer
10/17/2009 06:46:40 PM · #3
Not used to doing geometry on a Saturday night....41538.46 km?

10/17/2009 06:50:59 PM · #4
lol, i know me neither!

How did you get that?

10/17/2009 06:52:22 PM · #5
Originally posted by cujee:

lol, i know me neither!

How did you get that?

He cheated and looked up the answer....
10/17/2009 06:53:18 PM · #6
Ahhh, I see, actually I'm not sure if that is the right answer.

Oh it is. well done then, I would like to know the steps cause i was thinking about it for an hour and didn't know how to do it.

Message edited by author 2009-10-17 18:54:40.
10/17/2009 06:54:39 PM · #7
Ok, first take the formula for arc length

Arc length= 2 pi*r*(c/360)

where r is the radius and c is the angle the arc covers in degrees.

Re-arrange to solve for r

Plug in what you know: Arc length = 1500km and c = 13 degrees (90-77)

That will give you the radius in km

From there use Circumference = 2*pi*r
10/17/2009 07:29:02 PM · #8
Originally posted by Spazmo99:

Ok, first take the formula for arc length

Arc length= 2 pi*r*(c/360)

where r is the radius and c is the angle the arc covers in degrees.

Re-arrange to solve for r

Plug in what you know: Arc length = 1500km and c = 13 degrees (90-77)

That will give you the radius in km

From there use Circumference = 2*pi*r


everything sounds alright, except
c = 13 = 90 -77.

the c in your formula is angle to observer from earth center, not angle of sun for observer.

is the way you calculated c correct??

10/17/2009 07:49:03 PM · #9
The arc difference between the two cities is 13 degrees (90-77). 13 degrees = 13/360 of the total circumference and also equals 1500 miles. Therefore the circumference = 1500 miles x 360/13 = 41538.46 km.
10/17/2009 07:52:37 PM · #10
This smacks of a kid cheating on his high school homework.

Shame on all of you.

:-P
10/17/2009 07:54:46 PM · #11
Originally posted by Strikeslip:

This smacks of a kid cheating on his high school homework.

Shame on all of you.

:-P


What "last post"?

Shame on you!

R.
10/17/2009 07:57:08 PM · #12
Originally posted by Bear_Music:

Originally posted by Strikeslip:

This smacks of a kid cheating on his high school homework.

Shame on all of you.

:-P


What "last post"?

Shame on you!

R.

Hold on... this is my last, last, last post EVER!
10/17/2009 08:00:09 PM · #13
Originally posted by Strikeslip:

Originally posted by Bear_Music:

Originally posted by Strikeslip:

This smacks of a kid cheating on his high school homework.

Shame on all of you.

:-P


What "last post"?

Shame on you!

R.

Hold on... this is my last, last, last post EVER!


Define EVER.
10/17/2009 09:19:38 PM · #14
Originally posted by ErikV:

The arc difference between the two cities is 13 degrees (90-77). 13 degrees = 13/360 of the total circumference and also equals 1500 miles. Therefore the circumference = 1500 miles x 360/13 = 41538.46 km.


if the definition of angle of altitude given here is correct:

//susdesign.com/popups/sunangle/altitude.php

then above solution has to be wrong.

here is why.

consider triangle formed by three points
sun'c center
earth's center
observer's position.

Lets call angles at these corners as
Sun_A, Earth_A, Ob_A

We know that

Sun_A + Earth_A + Ob_A = 180.

Now this page says altitude of sun is angle with HORIZONTAL plane.
This horizontal plane has to be tangent to earth surface.
Which means that

Ob_A = 90 + 77 (altitude angle + plane's angle 90).

it implies that Earth_A + Sun_A = 180 - (90 - 77 ) = 13.

it means that Earth_A < 13.

in the solution that you guys have presented so far, Earth_A = 13, which is simply not possible. (because Sun_A > 0 ).

10/17/2009 09:19:57 PM · #15
Originally posted by cpanaioti:

Define EVER.


For him...the nanosecond he has between thinking about pressing the enter key and actually pressing it. :)

Message edited by author 2009-10-17 21:21:09.
10/17/2009 09:46:20 PM · #16
Originally posted by Strikeslip:

This smacks of a kid cheating on his high school homework.

Shame on all of you.

:-P

Hey, he said he worked on it for an hour and could not get the answer. So consider it tutoring.

And keep in mind that ' . substr('//www.dpchallenge.com/images/user_icon/21.gif', strrpos('//www.dpchallenge.com/images/user_icon/21.gif', '/') + 1) . ' cujee was the inventor of the DPC Olympics, which was a lot of fun and entertained a lot of people, so we as a community owe him one.
10/17/2009 09:50:46 PM · #17
Originally posted by Strikeslip:

Originally posted by Bear_Music:

Originally posted by Strikeslip:

This smacks of a kid cheating on his high school homework.

Shame on all of you.

:-P


What "last post"?

Shame on you!

R.

Hold on... this is my last, last, last post EVER!


This is like the endless series of Farewell Tours by Cher back in the day, or Favre's retirements....
10/17/2009 09:51:17 PM · #18
Can anyone here help me with my uranium enrichment project?
10/17/2009 09:54:40 PM · #19
Originally posted by Art Roflmao:

Can anyone here help me with my uranium enrichment project?

I can help you turn lead into gold, but I don't do nuclear stuff. Sorry.
10/17/2009 10:03:39 PM · #20
Originally posted by Art Roflmao:

Can anyone here help me with my uranium enrichment project?


contact iran.
10/17/2009 10:52:44 PM · #21
Originally posted by Art Roflmao:

Can anyone here help me with my uranium enrichment project?


I've got a couple of reactors in Western NC that can get you Plutonium much quicker. But, if you're stuck on uranium I've got several thousand calutrons that I was planning to sell to Iran. At about 138,000 US a piece I'd need a 10 percent down payment in advance before loading them on the train cars. For no charge I would remove the 2 pound blocks of C4 that were rigged to detonate after several hours of operation. A small parachute should drift down into your yard overnight with my contact information. Only call after 8am and before 9pm Eastern Daylight time please. I have several other enquirers into these units world wide so please reply promptly. I may give them priority as I wouldn't need to remove the explosives if I sold them overseas.
10/17/2009 11:01:21 PM · #22
Originally posted by zxaar:

Originally posted by Spazmo99:

Ok, first take the formula for arc length

Arc length= 2 pi*r*(c/360)

where r is the radius and c is the angle the arc covers in degrees.

Re-arrange to solve for r

Plug in what you know: Arc length = 1500km and c = 13 degrees (90-77)

That will give you the radius in km

From there use Circumference = 2*pi*r


everything sounds alright, except
c = 13 = 90 -77.

the c in your formula is angle to observer from earth center, not angle of sun for observer.

is the way you calculated c correct??


yes
10/17/2009 11:09:12 PM · #23
"It was my understanding that there would be no math."

Chevy Chase as Gerald Ford, SNL
10/17/2009 11:23:40 PM · #24
Originally posted by cujee:

Here is the question for people who enjoy science and understand geometry as well:

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 77 degrees

What is the circumference


you guys completely misunderstood the question. He's not looking for the circumference of the nearth, he's looking for the circumference of the sun. He says ..."the altitude of your sun is 77 degrees. What is the circumference?"

Back to the drawing board people! :P
10/17/2009 11:33:34 PM · #25
Originally posted by vawendy:

Originally posted by cujee:

Here is the question for people who enjoy science and understand geometry as well:

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 77 degrees

What is the circumference


you guys completely misunderstood the question. He's not looking for the circumference of the nearth, he's looking for the circumference of the sun. He says ..."the altitude of your sun is 77 degrees. What is the circumference?"

Back to the drawing board people! :P


Nawp....

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1500 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 77 degrees

What is the circumference


He wants the circumference of Nearth. Impossible to calculate circumference of sun from these data anyway.

R.
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