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 diamter 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. a. halfway around. b. 1/10 of the way around. c. 5/6 of the way around. d. 6.65 full revolutions.

Solution

Height of centre = radius + height above ground = (492/2) + 50 = 296 feet

Height of the person can be given by :

h(x) = 296 - 246cos(2pi*x) where amplitude = radius = 246 feet

x = 0 ; h(x) = 296 - 246(1) = 50 feet

a) halfway around : x=1/2 h(x) = 296 -246cos(2pi*0.5) = 296 -246(-1) = 542 feet

b) 1/10 of the way around: x = 1/10 ; h(x) = 296 -246cos(2pi*0.1)

= 96.98 feet

c) 5/6 th of the way around

x = 5/6 ; h(x) = 296 -246cos(2pi*0.833) = 173 feet

d) 6.65 revolutions = 6 revolutions + 0.65 revolution

x = 0.65 ; h(x) = 296 -246cos( 2pi*0.65) = 440.59 feet