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)=25sin(( )πt+( )*π)+29 reset 0 0.5 - 0.5

Explanation:

Step1: Determine the amplitude

The diameter of the Ferris - wheel is 50 meters, so the radius (amplitude $A$) is $\frac{50}{2}=25$ meters.

Step2: Calculate the angular frequency

It takes 6 minutes to do 3 revolutions. One revolution is $2\pi$ radians. So the angular frequency $\omega$: The number of revolutions per minute is $\frac{3}{6}=\frac{1}{2}$ revolutions per minute. In radians per minute, $\omega = 2\pi\times\frac{1}{2}=\pi$ radians per minute.

Step3: Find the vertical shift

The Ferris - wheel sits 4 meters above the ground and the radius is 25 meters. The center of the Ferris - wheel is at $4 + 25=29$ meters above the ground. So the vertical shift $D = 29$.

Step4: Determine the phase shift

He enters at the low - point when $t = 0$. For a sine function $y = A\sin(\omega t+\varphi)+D$, when $t = 0$, $y$ is at its minimum. The sine function $y=\sin x$ is at its minimum when $x = \frac{3\pi}{2}+2k\pi,k\in\mathbb{Z}$. For $y = A\sin(\omega t+\varphi)+D$, when $t = 0$, $\omega t+\varphi=\varphi$. So $\varphi=-\frac{\pi}{2}=- 0.5\pi$.

Answer:

$h(t)=25\cdot\sin(\pi t - 0.5\pi)+29$
So the blanks should be filled as follows: 25, 1, - 0.5, 29.