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This is a circular ferris wheel, with diameter of 9 meters, and the axis mounted 12 meters off the ground. The equation is the height of the a point that starts out level with the axis, at 't' seconds after the wheel starts up.
Now here's where things start to go awry:
The period of the revolution is the time it takes for the angle inside the sine to change by 2pi .
20(t - pi/2) = 2pi
20t - 10pi = 2pi
20t = 12pi
t = 12pi/20 = 1.885 seconds
I can't help it. All I did was the math, and that was bullet-proof. It was up to whoever wrote the question to guarantee that the answer makes sense.
For one thing, I don't believe the 'pi/2' belongs inside the parentheses with the 't'. But even if we take the 'pi/2' out of the parentheses, that still only makes the period 3.183 seconds, which is still an uncomfortable number ... especially for the riders.

Answered by AL2006 | 2024-06-10

To determine how long it takes the Ferris wheel to make one full rotation, we need to analyze the function representing the height of a rider over time, which is h(t) = 9sin(20(t-π/2))+12.
The function inside the sine, 20(t-π/2), represents the angular motion of the wheel.
For one full rotation, this angle should change by 2π radians.
Since the coefficient of t within the sine function is 20, it implies that the Ferris wheel completes 20 radians of rotation every second.
To find the time for one full rotation, we set the angular change equal to 2π radians:
20t = 2π
t = π/10 seconds
Thus, the Ferris wheel takes π/10 seconds to make one full rotation.

Answered by IanMckellen | 2024-06-24

The Ferris wheel takes approximately 10 π ​ seconds, or about 0.314 seconds, to make one full rotation, as derived from the sine function in the given height equation.
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Answered by AL2006 | 2024-09-26

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Answered by dnfd | 2025-07-12