a ferris wheel is 15 meters in diameter and boarded from a platform that is 5 meters above the ground. the…
a ferris wheel is 15 meters in diameter and boarded from a platform that is 5 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 2 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).\n\nf(t) =\n\nquestion help: video\n\nquestion 8\n\nmatch each graph with its equation. not all equations will be used.
Answer
Explanation:
Step1: Determine the amplitude
The diameter of the Ferris - wheel is 15 meters, so the amplitude $A=\frac{15}{2}=7.5$ meters.
Step2: Determine the vertical shift
The platform is 5 meters above the ground, and the center of the Ferris - wheel is at a height of $5 + \frac{15}{2}=5 + 7.5 = 12.5$ meters above the ground. So the vertical shift $D = 12.5$ meters.
Step3: Determine the period
The wheel completes 1 full revolution in 2 minutes. The formula for the period $T$ of a sinusoidal function is $T=\frac{2\pi}{B}$. Since $T = 2$, then $2=\frac{2\pi}{B}$, and solving for $B$ gives $B=\pi$.
Step4: Determine the phase shift
The six - o'clock position is level with the loading platform. We will use a cosine function (since at $t = 0$, the height is at the minimum value for a cosine - based model). The general form of a cosine function is $h=f(t)=A\cos(Bt - C)+D$. Since there is no horizontal shift in our starting condition, $C = 0$. The function is $h=f(t)=-7.5\cos(\pi t)+12.5$.
Answer:
$-7.5\cos(\pi t)+12.5$