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.





A wave passes through (0, 5), (30, 35), (45, 45), (60, 35), (90, 5), (120, 35), (135, 45), (150, 35), and (180, 5).

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

Answer: 30, 60, 120, and 150 seconds.

Work: model h(t)=25+20 sin((2π/90)t − π/2) (lowest at t=0). Set h=35 → sin(...) = 1/2, so (π/45)t − π/2 = π/6+2πk or 5π/6+2πk. Solving gives t = 30+90k and t = 60+90k. In 0 ≤ t ≤ 180 these are t = 30, 60, 120, 150.