Written homework problem 16
Assigned 10/29 and due 11/3
(From the spring 2013 take-home exam 3.)
You are located at (−10, 0) in a suburb of a city (whose downtown is located at the origin)
and you are driving to another suburb located at (0, 10). Because of a major event happening
downtown, the speed that you are able to drive depends on how close to downtown you are.
Suppose that when the car is located at (x, y), the speed you drive at that point is v(x, y).
p
Suppose that v(x, y) = x2 + y 2 . Compute the time required to get from (−10, 0) to (0, 10)
by (i) driving along the arc of the circle x2 + y 2 = 100, and (ii) driving along the straight line
from (−10, 0) to (0, 10). Which option takes less time? [ You might want to use Maple to
evaluate one or both of the integrals you get. ]
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