Question

A ferris wheel at the local fair has a diameter of 30 feet and a midline of 18 feet. this ferris wheel makes one revolution every 60 seconds. if amanda and steve are riding on this ferris wheel, which equation could be used to model d, the distance amanda and steve are from the ground as they ride the ferris wheel as a function of time, t?

Answer 1

Given that the ferris wheel has a diameter of 30 feet and a midline of 18 feet. This means that trough (minimum point) of the ferris wheel is at y = 18 - (30 / 2) = 18 - 15 = 3 i.e. the ferris wheel rotates about a minimum point at y = 3 and a maximum point at y = 33

Thus, the amplitude 30 and the vertical shift is 3.

Given that the ferris wheel makes one revolution every 60 seconds. This means that the phase angle is 360° / 60 = 60°/sec

If amanda and steve are riding on this ferris wheel, the equation that could be used to model d, the distance amanda and steve are from the ground as they ride the ferris wheel as a function of time, t is given by

$d=30\sin6\left(t+45\right)+33$