Problem

The boarding platform of a Ferris wheel is 3 meters above the ground and the Ferris wheel is 34 meters in diameter and spins once every 10 minutes.
How many minutes of the ride are spent higher than 24 meters above the ground? Round to two decimal places.

Answer

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Answer

Final Answer: The number of minutes of the ride spent higher than 24 meters above the ground is \(\boxed{0.76}\).

Steps

Step 1 :The Ferris wheel is a circle with a diameter of 34 meters, so the radius is 17 meters.

Step 2 :The center of the Ferris wheel is 20 meters above the ground (3 meters for the platform and 17 meters for the radius of the wheel).

Step 3 :Therefore, the part of the Ferris wheel that is higher than 24 meters above the ground is the part where the height of the seats is more than 4 meters above the center of the wheel (24 meters - 20 meters = 4 meters).

Step 4 :This corresponds to an angle of \(\arcsin(\frac{4}{17})\) in radians above and below the horizontal line through the center of the wheel.

Step 5 :We can calculate this angle, multiply by 2 (for the part of the wheel above and below the horizontal line), convert to degrees (since there are 360 degrees in a full circle), and then calculate the proportion of the 10-minute ride that is spent at this height.

Step 6 :Final Answer: The number of minutes of the ride spent higher than 24 meters above the ground is \(\boxed{0.76}\).

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