Question

select the correct answer from each drop - down menu. amare wants to ride a ferris wheel that sits four meters above the ground and has a diameter of 50 meters. it takes six minutes to do three revolutions on the ferris wheel. complete the function, h(t), which models amares height above the ground, in meters, as a function of time, t, in minutes. assume he enters the ride at the low point when t = 0. h(t)=< - sin(<πt+<π)+<

Explanation:

Step1: Find the amplitude

The diameter of the Ferris - wheel is 50 meters, so the radius $r = 25$ meters. The amplitude $A$ of the sine - function for the Ferris - wheel's height is the radius, so $A = 25$.

Step2: Find the vertical shift

The Ferris - wheel sits 4 meters above the ground, so the vertical shift $D$ is $4 + 25=29$ (the minimum height is 4 meters and the center of the Ferris - wheel is at a height equal to the radius above the minimum height).

Step3: Find the period

It takes 6 minutes to do 3 revolutions. The period $T$ for one revolution is $T=\frac{6}{3}=2$ minutes. The formula for the period of a sine function $y = A\sin(Bx - C)+D$ is $T=\frac{2\pi}{B}$. Since $T = 2$, we have $2=\frac{2\pi}{B}$, so $B=\pi$.

Step4: Determine the phase - shift

The person starts at the low - point when $t = 0$. For a sine function $y = A\sin(Bt - C)+D$, when starting at the low - point, the phase - shift $C$ is such that the function is of the form $y=-A\sin(Bt)+D$. Here, $C = 0$.
The height function $h(t)$ is $h(t)=25\sin(\pi t+\pi)+29$.

Answer:

$h(t)=25\sin(\pi t+\pi)+29$