Find a formula, using the sine function, for your height above ground after t minutes on the Ferris wheel.

Question

A Ferris wheel is 35 meters in diameter and boarded at ground level. The wheel completes one full revolution every 5 minutes. At t = 0 you are in the three o'clock position and ascending.

Answer 1

Given than in the 3 o'clock position the cabin is ascending, implies that

the wheel is turning in the counterclockwise direction.

Therefore the general formula for the height h(t) above ground is

h(t) = A + r×sin(2πt/T + φ)

where

A = 17.5 m is the height of the center above ground,

r = 17.5 m is the radius of the wheel,

T = 5 min is the period,

φ = 0 is the phase.

The value of the phase, φ, is obtained by fitting the function at t = 0, at which time

we are told h(0) = 17.5:

17.5 = 17.5 + 17.5×sin(2π×0/T + φ)

0 = 17.5×sin(φ)

φ = 0

Thus

h(t) = 17.5 + 17.5×sin(2πt/5)