A Ferris wheel is....

Question

A Ferris wheel is 15 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 1 full revolution in 8 minutes. How many minutes of the ride are spent higher than 14 meters above the ground?

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Answer 1

Hi Cynthia G.,

With the bottom of the Ferris Wheel being 5 meters off the ground, and a radius of, r = 7.5 meters, the center of the Ferris Wheel is 12.5 meters off the ground.

A horizontal line through the center of the Ferris Wheel is 12.5 meters off the ground, and therefore the lower half of the Ferris Wheel is always below 14 meters.

The distance from the horizontal to 14 meters is 1.5 meters (14 - 12.5), and angle between the horizontal and a radius to 14 meters is sin(θ) = 1.5/7.5 or θ = sin^-1(1.5/7.5) = 11.54^o. This angle height is on both sides of the Ferris Wheel and therefore 180^o + 2*11.54^o = 203.07^o is always under 14 meters. What is above 14 meters is 360^o - 203.07^o = 156.93^o.

Since it takes 8 minutes for 1 revolution, (156.93^o/360^o)*8 min ≈ 3.5 min, the amount of time the Ferris Wheel is above 14 meters.

I hope this helps, Joe.