A ferris wheel is 45 meters in diameter and boarded from a platform that is 4 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? metersWhat is the Midline? y = metersWhat is the Period? minutesHow High are you off of the ground after 4 minutes? meters
Question
A ferris wheel is 45 meters in diameter and boarded from a platform that is 4 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? metersWhat is the Midline? y = metersWhat is the Period? minutesHow High are you off of the ground after 4 minutes? meters
Solution
The amplitude of the Ferris wheel is half of the diameter, which is 45/2 = 22.5 meters.
The midline is the average of the maximum and minimum heights. The maximum height is the diameter plus the height of the platform (45 + 4 = 49 meters) and the minimum height is the height of the platform (4 meters). So, the midline is (49 + 4)/2 = 26.5 meters.
The period of the Ferris wheel is the time it takes to make one full revolution, which is 8 minutes.
To find out how high you are off the ground after 4 minutes, we need to know that the Ferris wheel starts at the minimum height and goes to the maximum height in the first half of the period (4 minutes). Since the Ferris wheel's motion is sinusoidal, after 4 minutes, you would be at the maximum height, which is 49 meters.
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