Trigonometric Function Ferris Wheel Word Problem

Question

As you ride a ferris wheel, your distance from the ground varies sinusoidally with time. When the last passenger boards the ferris wheel and the ride starts moving, let your position be modeled by the diagram provided.

Let t be the number of seconds that have elapsed since you began moving. It takes you 5 seconds to reach the top of the wheel (38 feet above the ground) and 20 seconds to make a complete revolution. The diameter of the wheel is 30 feet.

Work with your classmates to answer the following questions:

1. What is the lowest you go as the ferris wheel turns?
2. Why is this number always greater than zero?
3. Write the equation of a sinusoid that describes this motion.
4. Predict your height above the ground when t = 3, t = 8, t = 15, and t = 19

Answer 1

(1) The max height would be 38-30 = 8 ft off the ground

(2) It wouldn't be as good of a ride if you went negative, into the ground.

(3) A =15 is the amplitude, it is 1/2 of the diameter of the ferris wheel.

2π/B = time for one revolution, solving for B = π/10

C=5

D = 8 +15 = 23

y=15 sin π/10(t-5)+23

(4) Plugging in values into the equation

at t=3, y=14.2 ft

at t=15, y=23 ft

at t=19, y=8.7 ft