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Storm

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December 20, 2005
analytic geometrygraphing linesslopeAMCAIMEcalculusconics

Problem Statement

A car travels due east at 23\frac 23 mile per minute on a long, straight road. At the same time, a circular storm, whose radius is 51 miles, moves southeast at 122\frac 12\sqrt{2} mile per minute. At time t=0,t=0, the center of the storm is 110 miles due north of the car. At time t=t1t=t_1 minutes, the car enters the storm circle, and at time t=t2t=t_2 minutes, the car leaves the storm circle. Find 12(t1+t2).\frac 12(t_1+t_2).
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