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 ferries 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 250 mph; (iii) the lowest point on the ride should be c = 3 feet above the level ground. Find the radius of the ferris wheel. (Round your answer to two decimal places.) 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 theta with the horizontal, as pictured. It takes her 1.3 seconds to reach the top of the ride. Find the angle theta. (Round your answer to two decimal places.) Poor engineering causes Tiffs seat to fly off in 6 seconds. Describe where Tiff is located (an angle description) the instant she becomes a human missile. (Give your answer as an angle measured counterclockwise from her starting point P.)

Solution

12 rpm x ( 2r ft/ 1 revolution) x (1 mile / 5280 ft) x (60 minutes / 1 hour) = 250 miles / hour

(12r)/44 miles / hour = 250 miles/hour

(12r)/44 = 250

12r = 11000

r = 11000 / (12)

r = 291.78 ft. 583.56 ft diameter

From P to the top of the wheel takes 1.3 seconds. The period is 60/12 seconds (1 revolution).

1.3 sec / (60/12) = 0.26 of a revolution.

If you subtract ¼ of a revolution from that, you have the arc length intersected by .

0.25 - 0.25 = 0.01 revolution = 0.01 x 360° = 3.6°

Since from P to the top of the wheel takes 1.3 seconds, then from the top of the wheel until Tiff becomes a human missile is 4.7 seconds.

4.7 seconds / (60/12) = 0.94 revolutions. 0.94 x 360° = 338.4°