Simple math problem

[isaiahk9]

There are two versions of this question, one of which has never been solved. The really easy version goes like this :
A fenced, circular field has a radius of 30 m. A goat is tethered by a rope to a fence post at the edge of the field. If the goat can graze over exactly half the area of the field, how long is the rope?

I know that this is simple, and have solved similar questions before, but I just forgot how to solve it. If someone posts how to get this question, I'll post the un-solved version of this question.
thanx

[ecookman]

umm 15?

[S_Grimm]

15 what? Horses? bananas? Lets think about this. if the rope is 15 m long then that is the CENTER of the circle. that means he will graze in an ark, cutting below half the circle. the rope needs to be slightly longer so that there is compensation of the arc.

edit: i need to watch my measurements too!

[Insectoid]

Uh, if the rope is 30m long it will reach halfway. The radius of the circle is 30, you guys are using it as the diameter. 15m will reach a quarter of the way across the field. but that's as much as I can help.

[S_Grimm]

sorry. my teacher pointed that out to me too. your right. still the goat can only graze in an arc.

edit: i'm trying to post an image, but it on my machine. How do i do it?

[isaiahk9]

so, has anybody got it?

[Insectoid]

A/V: Upload it like you would a submission. Or, upload it to photobucket and post the IMG code.

EDIT: never mind, can't upload attachments in this board. Photobucket it is!

[btiffin]

Umm, as the old guy, out of school for decades now; don't think of this as simple math. It isn't. It includes some fairly substantial trig and converging limits.

If you convince me this isn't for homework, I can fill you in with a link.

Cheers

[isaiahk9]

@ btiffin : I thought it was b/c I found it in an old grade 10 textbook.

Convince you it isn't homework? I'll try :
1. If it was homework, I could've gone to the teacher, or I could check the back of the book for the answer.
2. I'm here asking not for an answer, but a way of doing it. even if this was homework, it would not be to answer the question, but to figure out how to do it.
3. If I know an unsolved version of this question, it probably isn't homework.
4. . . I'm out of ideas. Oh well, if I can't convince you, too bad.
---
There must be a simple way to solve it b/c there is a grade 10 student with a 50 or 60 something % in math and he found the answer.

[CodeMonkey2000]

This can't be in a grade 10 text book. And just because you have a 50-60% in a course doesn't mean you are stupid. And you could have jfgi.
link

[btiffin]

Ok;

This would be simple if the goat was tethered to the center of the field, but at the edge it gets complicated.

google gobbling goat

This explanation seems reasonable: http://plus.maths.org/issue9/puzzle/solution.html

The link I've shown will give you the answer, sadly. Well it will give you an answer using a 100m radius field. Changing to a 30m radius will be trivial.

Cheers

So, now I'd like to see the unsolved version ... you made me curious.

[isaiahk9]

thanx btiffin.

The unsolved version is just so mind-numbingly long that most people give up. Here it is :
A fenced field from a bird's-eye-view makes a scalene triangle with lengths of 64 meters, 52 meters and 79 meters. A goat is tethered onto the point between the 64 meter length and 52 meter length, and he can eat exactly one third of the grass.
However, there are complications. The point the goat is tethered at is the southmost point. Directly north of said point 10 meters, the ground forms a steep incline of 42 degress from its previous angle.
As well, 20 meters north of the goat is a patch of barren soil in the form of a perfect circle with a 2.6 meter radius.
The grass around the goat is 10 cm tall, and on the incline is 16 cm tall, besides the barren patch.
The rope that tethers the goat has a thickness of 3 centimeters, and is tied in a hangman's knot around the fence (which has a thickness of 15 centimeters), and a traditional Sprit Sail Sheet Knot on the goat's neck.
The goat has legs 20 cm tall, a chest and choulders 13 cm tall, a neck 10 cm long, a head 20 cm long, and a tongue which can grab grass 3 cm long. THis is needed to calculate exactly how much grass the goat can "reach" (how much grass its tongue can reach) (take into acount how easy or difficult it is for the goat to graze on the incline with this body structure, and on the flat plain).
Finally, every time the goat steps somewhere, the soil is compressed to 1 mm in that spot. And, every time the goat stretches the rope to its limit, its length increases by 6 mm.
So, taking into account the unusual shape of the fenced area, the difficulty/easiness of the goat to graze on an incline, the barren patch of ground, the rope around the neck of the goat and around the post, how the body type and length of the grass changes how it can graze, and how coninous movement will deepen the ground and stretch the rope, if by the goat's 12th try, and it can graze on exactly one third of the grass, how long is the rope tethering it
----
As you can see, it is not impossible, just really big.

[isaiahk9]

@CodeMonkey2000 - Nelson Mathematics 10, page 141 Challenge 2
I know that people who have 50% or 60% aren't (necessarily) stupid. Allow me to re-frase that sentence then :
A grade 10 student who has mediocre mathematic skills found a way to solve this question without doing it your way.
Happy?

[btiffin]

Now there is a problem a mathie could sink their teeth into.

Thanks isaiahk9

Umm, but I'm not a mathie anymore

And an old guy ramble note to everyone else

This is probably the type of problem an engineer planning the Mars Missions will have to deal with. So if you want to be on one of the teams that send people to Mars, try sinking your teeth into that beauty. Especially if you want to be on the team that sends the first goat to Mars.

Cheers

[ecookman]

woah tricky i was way off lol wasn't thinking