of the
Week
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Problem
of the Week |
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PROBLEM 214 |
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A local sports complex has an enormous flagpole at the
end of one of its fields. In order to raise the (equally enormous)
flag, they connect a line (in red) to the top of the flag, run the line to the top of
the flagpole, and then down to a small electric cart (in yellow) which pulls the flag up
as it is driven around the perimeter of a semicircular track at the end of
the field. See the figure on the left. Suppose the field is 150
ft across, the cart moves at a constant speed of 20 feet per second, and the
flag reaches the top exactly when the cart has reached the far side of the
field. At what speed is the flag rising when it is half-way up the
flagpole? When is the flag rising the fastest?
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