QuestionA ferris wheel is 32 meters in diameter and makes one revolution every 7 minutes. For how many minutes of any revolution will your seat be above 24 meters?
For minutes of any one revolution you will be above 24 meters.
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Studdy Solution
STEP 1
1. The ferris wheel is a perfect circle with a diameter of meters.
2. The center of the ferris wheel is at a height of meters (half the diameter) above the ground.
3. The ferris wheel makes one complete revolution every minutes.
4. We need to determine the time during which the seat is above meters.
STEP 2
1. Determine the height of the center of the ferris wheel.
2. Calculate the angle at which the seat is at meters.
3. Determine the proportion of the circle above meters.
4. Calculate the time spent above meters.
STEP 3
Determine the height of the center of the ferris wheel:
The center of the ferris wheel is at half the diameter above the ground:
STEP 4
Calculate the angle at which the seat is at meters:
The seat is at meters when the vertical distance from the center is:
Using the right triangle formed, calculate the angle using the cosine function:
Thus,
STEP 5
Determine the proportion of the circle above meters:
The total angle above meters is:
Convert this angle to a proportion of the circle:
STEP 6
Calculate the time spent above meters:
The time for one full revolution is minutes. Therefore, the time above meters is:
For minutes of any one revolution, you will be above 24 meters.
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