CPM Homework Help : CALC Problem 7-159

A Ferris wheel, $50$ feet in diameter, revolves at a rate of $2$ radians per minute. How fast is a passenger moving vertically when the passenger is $15$ feet higher than the center of the Ferris wheel and is rising?

Steps:

Sketch a diagram. Assume the wheel is rotating counterclockwise and let the passenger be at acute angle $θ$ and height $H$ above a horizontal radius. Do you see the right triangle? Write a geometric equation relating $H$ and $θ$ ? Then implicitly differentiate the equation with respect to time.

Hint:

$\frac{d\theta}{dt} =2$ . You are trying to solve for $\frac{dH}{dt}$ .

Partial Solution:

$h=25\sin(\theta)$
$\frac{dh}{dt}=25\cos(\theta)\frac{d\theta}{dt}$
Determine the value of $\operatorname{cos}(θ)$ when $h = 15$ ft.
Once you compute this value, use the differential equation to solve the problem.