SOLUTION: A Ferris wheel with a radius of 45 meters is elevated on a platform 5 meters above the ground. One full rotation takes 40 minutes. The height h(t) of a passenger is given by h(t) =
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Question 1209251: A Ferris wheel with a radius of 45 meters is elevated on a platform 5 meters above the ground. One full rotation takes 40 minutes. The height h(t) of a passenger is given by h(t) = 45sin(pi/20t) + 50. What is the first time t (in minutes) when the height is 72.5 meters? Answer by math_tutor2020(3817) (Show Source):
Solving 45w + 50 = 72.5 leads to w = 0.5 and it leads back to sin(pi*t/20) = 0.5
If sin(x) = 0.5 in radian mode, then x = pi/6 and x = 5pi/6 are two possibilities when considering the interval
This is something to memorize since it comes up a lot in trig. Alternatives are to use a reference sheet, unit circle, or a calculator.
We use the smaller of those x values since we're interested when the passenger reaches 72.5 meters the first time. If we changed "first time" to "second time", then we'd use 5pi/6 instead.
So,
sin(pi*t/20) = 0.5
sin(pi*t/20) = sin(pi/6)
pi*t/20 = pi/6
t/20 = 1/6
t = (1/6)*20
t = 20/6
t = 10/3
t = 3.3333... where the '3's go on forever
This is the number of minutes it takes to arrive at the first instance of being 72.5 meters above the ground.
Round that decimal value however your teacher instructs.
Or you can stick with the fraction form.
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