37. A 2 meter long piece of dental floss is pulled tight 1 meter above the ground. It is then relaxed by moving one end 175 mm. towards the other end. Assuming the sagged floss forms a circular arc, how far above the ground is the midpoint of the floss?
-Joseph Abbott
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06B Problem #37
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06B Problem #37
by PatriotAlanis » Tue May 01, 2007 5:35 pm
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by Kurt » Tue May 01, 2007 10:06 pm
The key to this problem is to realize in formula-form the two bits of information given:
The chord length of the circle is [unparseable or potentially dangerous latex formula].
The arc length known is [unparseable or potentially dangerous latex formula].
You have two equations with two variables - solve to find [unparseable or potentially dangerous latex formula].
With that, to find the distance you are looking for, use [unparseable or potentially dangerous latex formula] (find the height of the center using the first two terms, and subtract off the radius to find the height above the ground from the midpoint).
The chord length of the circle is [unparseable or potentially dangerous latex formula].
The arc length known is [unparseable or potentially dangerous latex formula].
You have two equations with two variables - solve to find [unparseable or potentially dangerous latex formula].
With that, to find the distance you are looking for, use [unparseable or potentially dangerous latex formula] (find the height of the center using the first two terms, and subtract off the radius to find the height above the ground from the midpoint).
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