Question

suppose that you want to model the height of a rider on a ferris wheel as a function of time. the amplitude of the function you use as a model should be equal to which of the following?
○ the area of the ferris wheel
○ the circumference of the ferris wheel
○ the diameter of the ferris wheel
○ the radius of the ferris wheel

Explanation:

Step1: Recall Amplitude in Ferris Wheel Model

The height of a rider on a Ferris wheel as a function of time is modeled by a sinusoidal function (e.g., \( y = A\sin(\omega t)+k \) or \( y = A\cos(\omega t)+k \)). The amplitude \( A \) represents the maximum displacement from the midline (average height) of the rider.

Step2: Relate to Ferris Wheel Dimensions

• The Ferris wheel is a circle. The radius of the circle is the maximum distance from the center (midline of the sinusoidal function) to the edge (where the rider is).
• The area (\( \pi r^2 \)) and circumference (\( 2\pi r \)) are not related to the amplitude (which is a linear measure of displacement). The diameter is \( 2r \), but the amplitude is the radius (since amplitude is the maximum distance from the midline, which is the center of the Ferris wheel, to the rider's position).

Answer:

the radius of the Ferris wheel