# Math

posted by Kori

At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 100 meters and a diameter of 50 meters. It takes the wheel seven 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 75 meters? Round the answer to the nearest second.

1. Reiny

amplitude is 25
let's use a sine curve function
h = 25sin kt
we want the period to be 7
2π/k = 7
k = 2π/7

so h = 25 sin 2π/7 t
the max of that curve is 25 but we want it to be 100
so we have to raise our function by 75

h = 25 sin 2π/7 t + 75 , where t is in minutes

Not sure what you mean by "If you start your ride at the midline"
Since the max height is to be 100m and the diameter is 50 m, then your lowest point and your entry point is 50 m above the ground.
so the axis of the ferris wheel must be 75 m above the ground.

So according to my interpretation, I have the following critical points
t=0, h = 50
t = (1/4)7 , h = 75
t = (1/2)7 , h = 100
t = (3/4)(7) , h = 75
t = 7 , h = 50

time to reach 75 m is 7/4 minutes or 1.75 minutes

I think the last part is all we really had to do, and I overthought the question.
I still would have had to do a phase shift to match my equation so that when t = 0 , h = 50

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