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 = 12 RPM; (ii) the linear speed of a rider should be 200 mph; (iii) the lowest point on the ride should be c = 3 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 1.4 seconds to reach the top of the ride. (Impose coordinates with units in feet.)

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 = 12 RPM; (ii) the linear speed of a rider should be 200 mph; (iii) the lowest point on the ride should be c = 3 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 1.4 seconds to reach the top of the ride. (Impose coordinates with units in feet.) a RPM c 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(233.427 cos(1.257t - 0.188) yt 3cos(1.257 0.188) x (b) Tiff becomes a human missile after 6 seconds on the ride. Find Tiffs coordinates the instant she becomes a human missile. (Round your answers to three decimal places.) (x(6), y(6) 231.507,29.879x (c) Find the equation of the tangential line along which Tiff travels the instant she becomes a human missile. (Round values to three decimal places as needed.) y-1 1.830x + 2.982 | x

Answer 1

4리 6o rad 231 333 2 う0- o.iss 中 tastt

6 sconds hnd = 1.8 1.6 820 4 → c= a 66-103.