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/