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Math 124 Quiz 6 Oct. 27, 2006
Name:
1)
A woman at a point
A
on the shore of a circular lake with radius 2 miles wants to arrive at the point
C
diametrically opposite
A
on the other side of the late in the shortest possible time. She can walk around the
shore of the lake at the rate of 4 miles per hour and row a boat at 2 miles per hour. At what angle
θ
(see
diagram) should she launch her boat to minimize time?
Solution:
(ON NEXT PAGE)
1
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View Full DocumentThis problem is tricky to be sure, so I felt it was reasonable to walk about the room and give people hints
here and there.
We begin by constructing a function for the total time it takes to complete her journey from point
A
to point
B
. This needs to be a function of the angle
θ
. This involves ﬁnding the distances involved
as
functions of
θ
. Let
x
represent the distance she needs to row. Using cosine, we see that
cos(
θ
) =
x
4
(This is because any triangle inscribed in a circle with one side on a diameter is a right triangle.) So,
x
= 4 cos(
θ
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 Spring '08
 KENNEDY
 Math, Calculus

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