Question

a ferris wheel is 50 meters in diameter and boarded from a platform that is 4 meters above the ground. the six oclock position on the ferris wheel is level with the loading platform. the wheel completes 1 full revolution in 4 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 2 minutes? meters question help: video

Explanation:

Amplitude:

Step1: Recall amplitude definition

Amplitude of a Ferris wheel (a sinusoidal motion) is half the diameter, as it's the maximum distance from the midline.
The diameter is 50 meters, so amplitude \( A=\frac{\text{diameter}}{2} \).

Step2: Calculate amplitude

\( A = \frac{50}{2}=25 \)

Midline:

Step1: Understand midline

Midline is the average of the maximum and minimum heights. The minimum height is the platform height (4 meters), and the maximum height is platform height + diameter (4 + 50 = 54 meters). Midline \( y=\frac{\text{min}+\text{max}}{2} \), or since amplitude is 25 and minimum is 4, midline is minimum + amplitude (or maximum - amplitude).

Step2: Calculate midline

Using minimum + amplitude: \( 4 + 25 = 29 \). Or \( \frac{4 + 54}{2}=\frac{58}{2}=29 \).

Period:

Step1: Recall period definition

Period is the time for one full revolution. The wheel completes 1 revolution in 4 minutes, so period \( T = 4 \) minutes.

Height after 2 minutes:

Answer:

s:
Amplitude: \(\boldsymbol{25}\) meters
Midline: \( y = \boldsymbol{29} \) meters
Period: \(\boldsymbol{4}\) minutes
Height after 2 minutes: \(\boldsymbol{54}\) meters