Gregor, the cockroach, is on the edge of a Ferris wheel that is rotating at a rate of 2 rev/min (counterclockwise as you observe him). Gregor is crawling along a spoke toward the center of the wheel at a rate of 3 in/min.
(a) Using polar coordinates with the center of the wheel as origin, assume that Gregor starts (at time t = 0) at the point r = 20 ft, θ = 0. Give parametric equations for Gregor’s polar coordinates r and θ at time t (in minutes).
(b) Give parametric equations for Gregor’s Cartesian coordinates at time t.
(c) Determine the distance Gregor has traveled once he reaches the center of the wheel. Express your answer as an integral and evaluate it numerically.
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