Associated Topics || Dr. Math Home || Search Dr. Math

### Ferris Wheel

```
Date: 08/11/97 at 18:37:50
From: Rhiannon
Subject: Finding how high in the air you are

Al and Betty are on a ferris wheel.  The wheel there has a radius of
15 feet and its center is 20 feet above ground level. You can describe
various  positions on the wheel as if the wheel was a clock.

How far off the ground are Al and Betty when they are:

a. at the 3 o'clock position
b. at the 12 o'clock position
c. at the 9 o'clock position
d. at the 6 o'clock position?
```

```
Date: 08/12/97 at 07:50:10
From: Doctor Jerry
Subject: Re: Finding how high in the air you are

Hi Rhiannon,

If t is any angle between 0 and 2pi, and t is in "standard position"
(vertex at the origin of an (x,y)-plane, the initial side is the
positive x-axis, and the terminal side is rotated counterclockwise
from the initial side through t radians), and r is a positive number,
then the point on a circle with center at the origin and radius r is

x = r*cos(t)
y = r*sin(t)

As t varies from 0 to 2pi, this point moves counterclockwise from
(r,0) back to (r,0). So, this is the ferris wheel. You want r = 15 and
to y you need to add 20, so that

x = 15*cos(t)
y = 20+15*cos(t).

The 3 o'clock position corresponds to t = 0, right?  The y is how far
off the ground they are.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Trigonometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search