A ferris wheel is 50 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn.
What is the Amplitude?
What is the Midline
What is the Period
How High are you off of the ground after 4 minutes?
A ferris wheel is 50 meters in diameter and boarded from a platform that is 2 meters above the ground.
so the axle is (50/2)+2 = 27 meters up. That's the mid-line, yeah?
and clearly the amplitude is 1/2 the diameter, or 25
so what else do you know?
To find the amplitude, midline, period, and height after 4 minutes, we need to analyze the given information.
1. Amplitude:
The amplitude of a periodic function represents the maximum displacement or distance from the midline. In this case, the amplitude is the radius of the ferris wheel.
Given that the ferris wheel has a diameter of 50 meters, the radius is half of that, which is 25 meters. So, the amplitude is 25 meters.
2. Midline:
The midline is the horizontal line through the center of the periodic function. In this case, it corresponds to the height above the ground when the wheel is at the six o'clock position.
Given that the platform is 2 meters above the ground, the midline is at a height of 2 meters.
3. Period:
The period of a periodic function is the time it takes for one complete cycle or revolution. In this case, the ferris wheel completes one full revolution in 8 minutes.
Therefore, the period is 8 minutes.
4. Height after 4 minutes:
To find the height after 4 minutes, we can substitute t = 4 into the function h = f(t).
Since the ferris wheel starts at the midline (2 meters above the ground), we need to add the amplitude to the midline.
So, substituting t = 4:
h = f(4) = 25 * sin(2π * 4 / 8) + 2
Calculating the expression:
h = 25 * sin(π/2) + 2
h = 25 * 1 + 2
h = 25 + 2
h = 27 meters
Therefore, you would be 27 meters above the ground after 4 minutes.
To find the amplitude, midline, and period of this function, we need to consider the given information.
1. Amplitude: The amplitude of a periodic function is the distance from the midline to the highest or lowest point of the graph. In this case, the ferris wheel reaches its highest and lowest points when it rotates 180 degrees from the six o'clock position. The diameter of the ferris wheel is 50 meters, so the radius is half of that, which is 25 meters. Therefore, the amplitude is 25 meters.
2. Midline: The midline of a function is the horizontal line that represents the average value of the function. In this case, the midline is the loading platform, which is 2 meters above the ground. Therefore, the midline is at a height of 2 meters.
3. Period: The period of a function is the time it takes for one complete cycle. In this case, the ferris wheel completes one full revolution in 8 minutes, which represents one cycle. Therefore, the period is 8 minutes.
4. Height after 4 minutes: To find your height above the ground after 4 minutes, we need to use the function h = f(t). Since the midline is at 2 meters, the height above the ground is given by the function h(t) = 25 sin(t) + 2. Plugging in t = 4, we get h(4) = 25 sin(4) + 2 ≈ 12.6 meters.
Therefore, the answers to your questions are:
- Amplitude: 25 meters
- Midline: 2 meters
- Period: 8 minutes
- Height after 4 minutes: Approximately 12.6 meters.