Answer:
a. The Ferris wheel has a diameter of 30 meters, which means the radius is 15 meters. Since the wheel is boarded from a platform that is 2 meters above the ground, the center of the Ferris wheel is 2 + 15 = 17 meters above the ground.
The function h(t) gives a person's height in meters above the ground t minutes after the wheel begins to turn. Since the Ferris wheel completes one revolution in 10 minutes, the period of h(t) is 10 minutes.
The midline is the average value of the function h(t) over one period, and it is equal to the vertical displacement of the graph from the x-axis. Since the center of the Ferris wheel is 17 meters above the ground, the midline is h = 17 meters.
The amplitude of the function h(t) is the distance between the midline and the maximum or minimum value of the function. The maximum height a person can reach on the Ferris wheel is when they are at the very top of the wheel, which is 17 + 15 = 32 meters above the ground. The minimum height a person can reach on the Ferris wheel is when they are at the very bottom of the wheel, which is 17 - 15 = 2 meters above the ground. So the amplitude of h(t) is 15 meters.
Therefore, the amplitude is 15 meters, the midline is h = 17 meters, and the period is 10 minutes.
b. To find the height of a person after 5 minutes, we can plug t = 5 into the function h(t):
h(5) = 15 sin(2π/10 * 5) + 17
h(5) = 15 sin(π) + 17
h(5) = 2 meters
Therefore, a person is 2 meters above the ground after 5 minutes on the Ferris wheel.
Explanation: