Question

John has been hired to design an exciting carnival ride. Tiff, the carnival owner, has decided to create the world's greatest Ferris wheel. Tiff isn't into math; she simply has a vision and has told John these constraints on her dream: (i) the wheel should rotate counterclockwise with an angular speed of a = 13 RPM; (ii) the linear speed of a rider should be 200 mph; (iii) the lowest point on the ride should be c = 5 feet above the level ground. The wheel starts turning when Tiff is at the location P, which makes an angle θ with the horizontal, as pictured. It takes her 1.5 seconds to reach the top of the ride. (Impose coordinates with units in feet.)

(a) Impose a coordinate system with the origin at the center of the wheel. Find the coordinates T(t) = (x(t), y(t)) of Tiff at time t seconds after she starts the ride. (Round values to three decimal places as needed.) x(t) = y(t) =

(b) Tiff becomes a human missile after 6 seconds on the ride. Find Tiff's coordinates the instant she becomes a human missile. (Round your answers to three decimal places.) (x(6), y(6)) =

(c) Find the equation of the tangential line along which Tiff travels the instant she becomes a human missile. ketch a picture indicating this line and her initial direction of motion along it when the seat detaches.

Answer 1