A Cow is tied to a barn...

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Part 1:
A cow is tethered to one corner of a square barn, 10 feet by 10 feet, with a rape 100 feet long. What is the maximum grazing area of the cow?

Part 2:
If the barn in Part 1 is rectangular, 10 feet by 20 feet, what is the maximum grazing area for the cow?

(I think I got part 1... 31,144 sq. ft.? Need confirmation though)

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Part 1: 31 145.149333 (feet^2) ~ close enough!

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I get:

1. 31145.15156
2. 30972.76091

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Do you mind explaining, how you got to this solution...
I am a bit lost here...

I arrive at 30508,08 square feet for question 1.

I calculated 3/4 circle with radius 100 feet.
Then twice 1/8 circle with radius 90 feet.
Then two triangles with sides 10 and 90 feet and an angle of 135°...

Where is my error (if any)...

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Just realised, I don't have 1/8 circles, but circle pieces with an angle of approx 49.5°

Just a min, will get my calculator out...

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OK, I am with you now: approx. 31144 square feet

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Bohne wrote:

Where is my error (if any)...

I admire your optimism. Laughing

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I just want to know what the heck someone is tying up a cow for Laughing

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What if the cow breaks it's tether?

Exactly how do you tether a cow to the corner of a barn anyway?

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Can you explain in-depth how you got the second part?

A diagram would be helpful Laughing

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Questions, questions; always with the questions you are making. What do you wanna know for, are you into bondage? Shocked

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Re: A Cow is tied to a barn...

TehMeh wrote:

Part 1:
A cow is tethered to one corner of a square barn, 10 feet by 10 feet, with a rape 100 feet long. What is the maximum grazing area of the cow?

Part 2:
If the barn in Part 1 is rectangular, 10 feet by 20 feet, what is the maximum grazing area for the cow?

(I think I got part 1... 31,144 sq. ft.? Need confirmation though)

Why would they be tying up the cow? Perhaps you should reread the first sentence. It might explain much.

I wondered how much grazing a cow would actually be doing during a 100 foot long rape. Shouldn't the answer be zero?

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rope rape......... same thing Laughing

parados I am joking so don't explain okay?

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TehMeh wrote:

Can you explain in-depth how you got the second part?

A diagram would be helpful

You can always ask this cow Laughing

http://img144.imageshack.us/img144/8682/cowwithredbarnle9.jpg

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Wow... what a grave typo.

Well, the question should say rope. Guess Freud would say that I'm into beasitality.

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TehMeh wrote:

Wow... what a grave typo.

Well, the question should say rope. Guess Freud would say that I'm into beasitality.

That was cute Laughing

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Unfortunately there is missing information in the problem. We don't know how the rope is attached to the cow.

If the rope is attached to a collar around the cows neck the cow will be able to graze about 3' beyond the end of the rope.
If the rope itself is tied around the cow's neck then the length from the barn to the cow will be about 6' less and the cow can graze 3' beyond that.
If the rope is attached to the cows hind leg it will be able to graze about 8' beyond the rope.
If attached to the cows tail then it can graze about 10' beyond the rope.

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What if it is attached by its ear?

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TehMeh wrote:

Can you explain in-depth how you got the second part?

A diagram would be helpful

I had:
the corners of the barn at:
(0,0), (0,10), (20,0), (20,10)
and the cow tethered at (0,10)

I computed the intersection of these circles:
x^2 + y^2 = 90^2
(x-20)^2 + (y-10)^2 = 80^2

Then it's a matter of computing the angles for the sectors of the circles of radius 90 and 80. Throw in the areas of the two triangles (20, 90, L and 10, 80, L) and you're done.

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Can the cow get into the barn? Would it want to?
Are the barn doors open or closed?

Is there hay inside the barn?

What kind of material is the rope made from? ie could it stretch?

What about the slope factor? If the barn was on a hillside there would be a slop factor.

Quote:

What if it is attached by its ear?

Or ring through its nose. Thats not uncommon.

There would have to be a water trough and the area around said trough would be either trampled aor ungrazeable so subtract a couple of square meters for that.

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A Cow is tied to a barn...

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