   Chapter 3.9, Problem 46E

Chapter
Section
Textbook Problem

A Ferris wheel with a radius of 10m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when his seat is 16 m above ground level?

To determine

To find: The rate at which the height of the rider is rising when his seat is 16 m above the ground level.

Explanation

Given:

The Ferris wheel of radius 10 m is rotating 1 revolution in every 2 minutes.

Formula used:

(1) Chain rule: dydx=dydududx

(2) Pythagorean Theorem

Calculation:

Let us assume that O be the centre of the Ferris wheel and B be the lowest point on the circumference of the Ferris wheel and A be the position of the rider seat which is h  m from the centre of the wheel and θ be the angle to the rider seat from the horizontal as shown in the Figure 1 given below.

Since the angle θ and the height h increase with the time t, the angle θ and height h are the function of the time t.

From the above triangle,

sinθ=h10h=10sinθ

When the height of the rider 16 m from the ground that is h=6m.

x=10262[QByPyhtagoreanTheorem]=10036=64=8m

Differentiate h with respect to the time t

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