John has been hired to design an exciting carnival ride Tiff

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: the wheel should rotate counterclockwise with an angular speed of a = 15 RPM; the linear speed of a rider should be 200 mph; the lowest point on the ride should be c = 4 feet above the level ground. Find the radius of the ferris wheel. (Round your answer to two decimal places.) 186.74 ft Once the wheel is built, John suggests that Tiff should take the first ride. The wheel starts turning when Tiff is at the location P, which makes an angle 0 with the horizontal, as pictured. It takes her 1.3 seconds to reach the top of the ride. Find the angle 6. (Round your answer to two decimal places.)

Solution

(a) Revolutions per minute to miles per hour and solve for the radius:
15 rpm ·( 2r ft/ 1 revolution)· (1 mile / 5280 ft) · (60 minutes / 1 hour) = 200 miles / hour
=> (15r)/44 miles / hour = 200 miles/hour
=> (15r)/44 = 200
=> r = 1760/(3pi)
therefore, radius=r = 186.74 ft.
(b) From P to the top of the wheel takes 1.3 seconds. The period is 60/15 seconds (1 revolution). 1.3 sec / (60/15) = .325 of a revolution. If you subtract ¼ of a revolution from that, you have the arc length intersected by . .325 - .25 = .075 revolution = .05·360° = 27°