Question

A ferris wheel with a diameter of 100 feet rotates at a constant rate of 4 revolutions per minute. Let the center of the ferris wheel be at the origin.

1. Each of the ferris wheel's cars travels around a cirlce.
a) Write an equation of the circle where x and y are measured in feet.
b)sketch a graph of an equation you wrote in part (a)
c) Use the vertical line test to determine whether y is a function of x.
d) What does your answer to part (C) mean in the context of the problem?

Answer 1

1a. (x-h)^2 + (y-k)^2 = r^2.

C(h,k) = C(0,0).

Eq: x^2 + Y^2 = (50)^2 = 2500.

b. Use these points for graphing:
Angle (X,Y)
0. (5,0)
45. (3.54,3.54)
90. (0,5)
135 (-3.54,3.54)
180 (-5,0)
225 (-3.54,-3.54)
270 (0,-5)
315 (3.54,-3.54)

Sample Calculations
Scale for radius(r) = 0.1 * 50 = 5Ft.

X = r*cosA = 5*cos(0) = 5.
Y = 5*sin(0) = 0.

X = 5*cos45 = 3.54.
Y = 5*sin45 = 3.54.