a ferris wheel is 50 meters in diameter with the bottom of the wheel 1 meter off the ground it makes a full revolution in 12 minutes.

What function would track the height above the ground for a point that is at the bottom of the wheel when it starts moving?

To track the height above the ground for a point at the bottom of the Ferris wheel when it starts moving, you need to understand the movement of the wheel.

Given that the diameter of the Ferris wheel is 50 meters and the bottom of the wheel is 1 meter off the ground, we can find the radius of the wheel by dividing the diameter by 2. So, the radius is 50/2 = 25 meters.

Since the Ferris wheel makes a full revolution in 12 minutes, we can assume it completes one cycle every 12 minutes.

To create a function that tracks the height above the ground, we can use a trigonometric function like sine or cosine to model the vertical motion of the point on the Ferris wheel. Since we know that one cycle takes 12 minutes to complete, we can set the period of the function to be 12 minutes.

The general equation for a function that describes vertical motion as a function of time is:

h(t) = A * sin(2π * t / T) + k

where:
- h(t) represents the height above the ground as a function of time,
- A is the amplitude (the maximum value of the function),
- t is the time in minutes,
- T is the period of the function (12 minutes in this case),
- k is a vertical shift or offset.

In this case, when the point is at the bottom of the wheel, the height above the ground is 1 meter. This means that the vertical shift or offset (k) is 1.

So, the specific equation for tracking the height above the ground for a point at the bottom of the Ferris wheel when it starts moving would be:

h(t) = 25 * sin(2π * t / 12) + 1

where the amplitude (A) is taken as the radius of the Ferris wheel, 25 meters, and the vertical shift (k) is 1 meter.