perplexus.info :: Calculus : The horse and the grass field

The horse and the grass field (Posted on 2008-06-15)

A horse is tied at a point on the circumference of a circular grass field of radius r, by a rope with length L.

What is the length of the rope, in terms of r, so the horse can eat exactly half of the grass field?

Submitted by pcbouhid

Rating: 4.0000 (1 votes)

Solution: (Hide)

I finished with this equation, where k = L/r:

{arc sen [k * √(1 - k²/4)]} - { k/2 * (2 – k²) * √(1 - k²/4)} + {k² * arc sen [√(1 - k²/4)]} - {k³/2 * √(1 - k²/4)} = pi/2

Using Excel to solve it, I found k = L/r = 1,15872...

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2022-05-03 21:54:26
re: solution ------- something wrong	pcbouhid	2008-06-15 23:02:41
solution	Daniel	2008-06-15 21:06:19
A horse by a different color? (Spoiler)	Dej Mar	2008-06-15 15:51:24

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