Question

At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 50 meters and a diameter of 35 meters. It takes the wheel 5 minutes to make one revolution. If you start your ride at the midline and the ferris wheel rotates counter clockwise, how many seconds will it take for your seat to reach a height of 50 meters? Round the answer to the nearest second.
The period:
2π/k = 5
then k = 2π/5

the amplitude = 35/2 = 17.5

your ferris wheel behaves like
h = 17.5sin(2π/5)

but you said it is 50 m high and the max height of the function is 17.5
so we need h = 17.5sin(2π/5) + 32.5

looks like I am overthinking this question.
Since you want to be at a height of 50 m, that height is reached after 1/4 rotation
or (1/4)of 5 minutes which is 1.25 minutes or 75 seconds

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