John has been hired to design an exciting carnival ride. Tiff,the carnival owner, has decided to create the world's greatestFerris wheel. Tiff isn't into math; she simply has a vision and hastold John these constraints on her dream: (i) the wheel shouldrotate counterclockwise with an angular speed of a = 13 RPM; (ii)the linear speed of a rider should be 200 mph; (iii) the lowestpoint on the ride should be c = 5 feet above the level ground. Thewheel starts turning when Tiff is at the location P, which makes anangle ? with the horizontal, as pictured. It takes her 1.5 secondsto reach the top of the ride. (Impose coordinates with units infeet.)
(a) Impose a coordinate system with the origin at the center ofthe wheel. Find the coordinates T(t) = (x(t), y(t)) of Tiff at timet seconds after she starts the ride. (Round values to three decimalplaces 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 Tifftravels the instant she becomes a human missile. ketch a pictureindicating this line and her initial direction of motion along itwhen the seat detaches.
