Question 545126
At noon, the cruise ship Celebration is 60 miles due south of the cruise ship Inspiration and is sailing north at a rate of 30 mph. If the inspiration is sailing west at a rate of 20 mph, find the time at which the distance d between the ships is a minimum. What is this distance?
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{{{s(t) = sqrt((60 - 30t)^2 + (20t)^2) = sqrt(1300t^2 - 3600t + 3600)}}}
ds/st = {{{(1/2)*(1300t^2 - 3600t + 3600)^(-1/2)*(2600t - 3600) = 0}}} at min
ds/dt = 0 @ 2600t - 3600 = 0
--> t = 18/13 hours
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s(18/13) = 33.282 miles min distance