Question

A Ferris wheel is 48 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t). Assume that f(0) =1 Start your counting.

Answer 1

The height function for a passenger on a Ferris wheel 48 meters in diameter, starting 1 meter above the ground with a period of 2 minutes, is h = f(t) = 24 · cos(π · t / 2) + 24 + 1.

Step-by-step explanation:

To write an equation for the height h = f(t) of a passenger on a Ferris wheel, we need to account for the diameter of the wheel, the starting height, and the time it takes for one full revolution.

The diameter of the wheel is 48 meters, so the radius (r) is half of that, which is 24 meters. The platform is 1 meter above the ground, so the minimum height (h_min) is also 1 meter. The Ferris wheel completes one revolution in 2 minutes, so the period (T) is 2 minutes.

The equation for the height of a passenger above the ground, given these conditions and assuming sinusoidal motion, is:h = r · cos(π · t / T) + r + h_min

Substituting the given values in, we get:

h = f(t) = 24 · cos(π · t / 2) + 24 + 1

The cosine function is used here because the passenger starts at the lowest point (6 o'clock position), 1 meter above the ground, which corresponds to the minimum value of a cosine function that starts at 0 degrees or 0 radians.