I have absolutely no idea even where to start. Please help!

The carnival has come to town with a ferris wheel that has a radius of 30 feet. People get on when passenger compartments are at the lowest, 2 feet off the ground. The wheel makes a full revolution in 20 seconds.
Using a cosine function, write an equation modelling the height of a passenger from the ground as a function of time.

Thanks so much!

the wheel has a radius of 30, so

y = 30sint or 30cost

people get on at the bottom, so at t=0 y is at its minimum

y = -30cost

the minimum is at y=2, so

y = 32-30cost

the period is 20. y=cos(kt) has a period of 2π/k, so 2π/k = 20. k=π/10

y = 32-30cos(π/10 t)

see

http://www.wolframalpha.com/input/?i=32-30cos(%CF%80%2F10+t)

No problem! Let's break down the problem step by step and find a solution using a cosine function.

To start, we need to understand the basic characteristics of the ferris wheel. We know that the ferris wheel has a radius of 30 feet, and the passenger compartments are 2 feet off the ground when they are at the lowest point. This means that the highest point the passenger will reach is 32 feet above the ground.

Next, we need to determine the period of the ferris wheel. The period is the time it takes for one complete revolution of the ferris wheel. In this case, the wheel makes a full revolution in 20 seconds.

To model the height of a passenger from the ground as a function of time, we can use a cosine function. The general equation for a cosine function is:

y = A * cos(B(x - C)) + D

In this equation:
- A represents the amplitude of the function. In our case, since the height ranges from 2 to 32 (a total of 30 feet), the amplitude is 30/2 = 15.
- B represents the frequency of the function, or how many cycles it completes within a given time interval. Since the ferris wheel makes a full revolution in 20 seconds, the frequency is 2π/20 = π/10.
- C represents the horizontal shift of the function. In our case, it will be 0 since we start at t = 0.
- D represents the vertical shift of the function or the midpoint of the range. Since the lowest point is at 2 feet, D will be 2.

Using these values, the equation modelling the height of a passenger from the ground as a function of time can be written as:

y = 15 * cos((π/10)t) + 17

This equation will give you the height of a passenger above the ground at any given time. Just plug in the value of t, which represents the time in seconds, to calculate the corresponding height.