A Ferris wheel is 50 meters in diameter and boarded from a platform that is 5 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes one full revolution every 9 minutes. You make two complete revolutions on the wheel, starting at t = 0.

Graph h = f(t), where h is the height above the ground (in meters) at time t, in minutes. Indicate the period, the amplitude, and the midline of your graph. [Hint: first determine an appropriate interval for t, with t ≥ 0.]

Period is___minutes.

Amplitude is ___ meters.

Midline is h = ___ meters.

Period is 18 minutes.

Amplitude is 25 meters.

Midline is h = 30 meters.

To graph the height above the ground as a function of time, we need to understand the motion of the Ferris wheel.

Given:
- Diameter of the Ferris wheel = 50 meters, so the radius (r) = 25 meters.
- Platform height = 5 meters above the ground.
- One complete revolution takes 9 minutes.

The period of the Ferris wheel can be calculated as the time it takes to complete one revolution, which is 9 minutes.

The amplitude of the Ferris wheel can be calculated as half the difference between the maximum and minimum heights. Since the Ferris wheel initially starts at the 6 o'clock position, the maximum height occurs at 3 o'clock and 9 o'clock positions. At these positions, the radius + platform height = 25 + 5 = 30 meters. Similarly, the minimum height occurs at the 12 o'clock and 6 o'clock positions, where the radius - platform height = 25 - 5 = 20 meters. Hence, the amplitude is (30 - 20)/2 = 5 meters.

The midline of the graph is the average of the maximum and minimum heights, which is (30 + 20)/2 = 25 meters.

Now let's graph the function h = f(t), where h is the height above the ground at time t.

On the x-axis, we can represent time t in minutes, and on the y-axis, we can represent height h in meters.

Since the Ferris wheel makes two revolutions starting from t = 0, the appropriate interval for t is [0, 2*9] = [0, 18].

To graph the function h = f(t), we start at the midline height (25 meters) and then add or subtract the amplitude (5 meters) to find the maximum and minimum heights at different times.

At time t = 0, the height is at the midline (25 meters).
At time t = 9, the height reaches the maximum (25 + 5 = 30 meters).
At time t = 18, the height returns to the midline (25 meters).

The graph will be sinusoidal with a period of 9 minutes, an amplitude of 5 meters, and a midline at h = 25 meters.

Here is the graph:
```
^ .
| .
30 ---|----------.
| . .
| . .
25 ---|---------.-----.----- t
| . .
| .
20 ---|----------------.
0 9 18
```

Thus, the period is 9 minutes, the amplitude is 5 meters, and the midline is h = 25 meters.

To graph the function h = f(t), we need to understand the given information and analyze the Ferris wheel's movement.

1. Period:
The period is the time it takes for the Ferris wheel to complete one full revolution. In this case, the Ferris wheel completes one full revolution every 9 minutes. Therefore, the period is 9 minutes.

2. Amplitude:
The amplitude represents the height above the midline. Since the Ferris wheel has a diameter of 50 meters, the radius is half of that, which is 25 meters. The highest point on the Ferris wheel is when it is at the 12 o'clock position, which is 25 meters above the midline. The lowest point is when it is at the 6 o'clock position, which is 25 meters below the midline. Therefore, the amplitude is 25 meters.

3. Midline:
The midline represents the average height of the Ferris wheel. In this case, the loading platform is 5 meters above the ground, and the 6 o'clock position on the Ferris wheel is level with the loading platform. Therefore, the midline is at a height of 5 meters.

Now, let's graph the function h = f(t) using the given information.

- Choose an appropriate interval for t. In this case, we'll choose t values from 0 to 18 (two complete revolutions, with each revolution taking 9 minutes).
- Mark the midline (h = 5 meters) on the y-axis.
- Mark the highest point (amplitude) above the midline at 30 meters (25 meters above the midline).
- Mark the lowest point (amplitude) below the midline at -20 meters (25 meters below the midline).
- Connect the highest, lowest, and midline points to create a sinusoidal wave.

The completed graph should display a sinusoidal wave with a period of 9 minutes, an amplitude of 25 meters, and a midline at h = 5 meters.

I already did this today with a 7 minute period

anyway
They gave you PERIOD = 9 minutes

Amplitude = wheel radius = 25 meters

midline at 5 + 25 = 30 meters

h = 30 - 25 cos (2 pi t/T )