Question

a ferris wheel is 10 meters in diameter and boarded from a platform that is 3 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 6 minutes. the function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. write an equation for h = f(t). f(t) = question help: video

Explanation:

Step1: Determine the amplitude, midline, and period

• The diameter of the Ferris wheel is \(d = 10\) meters, so the radius \(r=5\) meters. The amplitude \(A = 5\).
• The midline \(C\) is the height of the center of the Ferris wheel. Since it is boarded from a platform \(3\) meters above the ground and the radius is \(5\) meters, \(C=3 + 5=8\).
• The period \(T = 6\) minutes. Using the formula \(B=\frac{2\pi}{T}\), we get \(B=\frac{2\pi}{6}=\frac{\pi}{3}\).

Step2: Choose the appropriate trigonometric function

Since we start at the lowest point (six - o'clock position), we use the cosine function with a negative sign. The general form of a cosine function is \(h(t)=A\cos(Bt)+C\).

Substituting \(A = 5\), \(B=\frac{\pi}{3}\), and \(C = 8\) into the formula, we get \(h(t)=- 5\cos(\frac{\pi}{3}t)+8\)

Answer:

\(f(t)=-5\cos(\frac{\pi}{3}t)+8\)