Ferris Wheel Problem

Question

Imagine you are riding a ferris wheel of radius 10m; the center of the wheel is 11m above the ground. Starting at the bottom of the wheel you ride around it counter-clockwise until the moment that you are 5m above the ground. At that instant suppose that your height above the ground is increasing at a rate of 4 m/s. What will your horizontal speed be at that same instant.

a. 0 m/s

b. 1 m/s

c. 2 m/s

d. 3 m/s

e. 4 m/s

f. 5 m/s

Answer 1

The equation of the circle that maps out the Ferris wheel would be x² + (y - 11)² = 100

Multiplying this out, we get x² + y² - 22y + 121 = 100 or x² + y² - 22y = -21

Now take the derivative implicitly with respect to time:

d(x² + y² - 22y) = 0

dt

2x•dx/dt + 2y•dy/dt - 22dy/dt = 0

solving for dx/dt we get:

dx/dt = [dy/dt(22 - 2y)]/(2x)

When y = 5, the x = 8 (draw a triangle and use the Pythagorean Theorem) so:

dx/dt = [4(22 - 2•5)]/(2•8) = 4•12/16 = 3