Question

A Ferris wheel has a diameter of 40 meters with its center 25 meters above the ground. It makes one complete rotation every 90 seconds.



The function and graph shown represent the height, h, of a car on a Ferris wheel, in meters, as a function of time, t, in seconds, assuming the car starts at the lowest point.

What are all the solutions of t for when the car is 35 meters high over the interval
0
≤
t
≤
180
?


30 and 60 only


22.5 and 67.5 only


30, 60, 120, and 150


22.5, 67.5, 112.5, and 157.5

Answer 1

h(t) = 25 − 20 cos((2π/90) t). Set h = 35:

25 − 20 cos((2π/90) t) = 35 → cos((π/45) t) = −1/2.

Cos = −1/2 at angles 2π/3 and 4π/3, so
t = (45/π)·(2π/3) = 30 and t = (45/π)·(4π/3) = 60,
and plus the period 90 gives 120 and 150.

Thus t = 30, 60, 120, 150.