Ferris WheelDate: 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/ |
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