### Home > APCALC > Chapter 7 > Lesson 7.3.6 > Problem7-168

7-168.

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? Homework Help ✎

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.

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

$h=25\sin(\theta)$

$\frac{dh}{dt}=25\cos(\theta)\frac{d\theta}{dt}$

Determine the value of cos(θ) when $h = 15$ ft.
Once you compute this value, use the differential equation to solve the problem.