Question

A ferris wheel is 10 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn.

What is the Amplitude? _________ meters
What is the Midline? y = _________ meters
What is the Period? ________ minutes
How High are you off of the ground after 3 minutes? meters

Answer 1

Minimum height of a ferris wheel above the ground, h_min = 4 m

Diameter of a ferris wheel, D = 10 m

(i) The amplitude which will be given by -

A = D / 2

A = [(10 m) / (2)]

A = 5 m

(ii) The midline which will be given by -

y = h_min + A

y = [(4 m) + (5 m)]

y = 9 m

(iii) How High are you off of the ground after 3 minutes?

h (t) = - A Cos t + y

where, = angular frequency = 2 / T

h = - (5 m) cos {[(2) / (6 min)] (3 min)} + (9 m)

h = - (5 m) cos () + (9 m)

h = [(5 m) + (9 m)]

h = 14 m