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