The Singapore Flyer is a Ferris wheel constructed on top of

The Singapore Flyer is a Ferris wheel constructed on top of a three-story building. The wheel itself has a diameter of 492 feet, but the bottom of the wheel sits nearly 50 feet off the ground. Determine the height from the ground of a person after boarding from the bottom and traveling each of the following portions of a revolution.† (Round your answers to the nearest foot.) (a) halfway around ft (b) 1/10 of the way around ft (c) 7/8 of the way around ft (d) 6.65 full revolutions ft

Solution

First, you need to compute the height of the center (50-foot clearance plus the radius). This is the center of the circle.

Now, add or subtract the height difference from that center, which will be the sine of the angle resulting from starting at straight down (negative y axis). You can also regard this as -cos (x), where x is the revolution amount. For instance, if you\'re working in degrees, then you get the following:

c = 50 + 492/2 = 296
h = c - cos(x) = 296 - cos(x)

(1) h = 296 - cos(360 * 1/2) = 297 ft
(2) h = 296 - cos(360 * 1/10) = 295.2 ft

(3) h = 296 - cos(360 * 7/8) = 295.3 ft
(4) h = 296 - cos(360 * 6.65) = 296.6 ft