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7-168.

A Ferris wheel, feet in diameter, revolves at a rate of radians per minute. How fast is a passenger moving vertically when the passenger is 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 and height above a horizontal radius. Do you see the right triangle? Write a geometric equation relating  and . Then implicitly differentiate the equation with respect to time.

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