# Related Rates: Ferris Wheel Program

• bfr
In summary, the question asks for the speed at which a person is falling when halfway to the bottom of a 120-foot diameter Ferris wheel that makes one complete revolution per minute. The solution involves understanding the circular path and the velocity at which the person is traveling along it. It is not necessary to set up a related rates problem.
bfr

## Homework Statement

You are riding a Ferris wheel 120 feet in diameter. It makes one complete revolution every minute. How fast are you falling when you are halfway to the bottom?

None

## The Attempt at a Solution

I really am not sure where to start. I'm actually not even completely sure what the question is asking...I'd think this would be a related rates problem, but the velocity is always constant. I tried setting up the parametric equations y=sin t and x=cos t and taking the derivatives of them...but that didn't really help. Also, when I'm half way to the bottom, the tangent to the Ferris wheel is vertical and I have the greatest velocity... Any ideas?

Last edited:
bfr said:
... when I'm half way to the bottom, the tangent to the Ferris wheel is vertical and I have the greatest velocity.

There's your starting point right there. How long is one trip around the Ferris wheel? Given how long it takes to happen, how fast are you traveling along this circular path? How does this answer the problem? (You could set up a related rates problem out of this, but it's really a lot of extra trouble...)

## 1. What is the purpose of a Ferris wheel program in related rates?

A Ferris wheel program is used to model the position of a person on a Ferris wheel over time. It helps to understand how the position, velocity, and acceleration of the person changes as the wheel rotates.

## 2. How does the height of the person on the Ferris wheel change with respect to time?

The height of the person on the Ferris wheel changes with respect to time due to the rotation of the wheel. As the wheel turns, the person moves up and down, resulting in a changing height. This can be represented by a position function in the Ferris wheel program.

## 3. What is the relationship between the velocity of the person and the velocity of the Ferris wheel?

The velocity of the person on the Ferris wheel is directly related to the velocity of the Ferris wheel. As the wheel turns, the person's velocity changes due to the changing direction of the wheel. This can be seen in the velocity function in the Ferris wheel program.

## 4. How can the acceleration of the person on the Ferris wheel be calculated using the program?

The acceleration of the person on the Ferris wheel can be calculated by taking the derivative of the velocity function in the Ferris wheel program. This will give the rate of change of the person's velocity, which is the acceleration.

## 5. Are there any limitations to using a Ferris wheel program for related rates?

While a Ferris wheel program can provide valuable insights into related rates problems, it has some limitations. It assumes that the wheel is a perfect circle and that the person is always at a fixed distance from the center of the wheel. In reality, there may be slight variations in the shape of the wheel and the positioning of the person, which can affect the accuracy of the results.

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