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Calculus / Calculus: Early Transcendentals 1 / Chapter 10.1 / Problem 26E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Solution: Circular motion Find parametric equations that

Chapter 8, Problem 26E

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QUESTION:

Find parametric equations that describe the circular path of the following objects. Assume (x, y) denotes the position of the object relative to the origin at the center of the circle. Use the units of time specified in the problem. There is more than one way to describe any circle.

A Ferris wheel has a radius of 20 m and completes a revolution in the clockwise direction at constant speed in 3 min. Assume that x and y measure the horizontal and vertical positions of a seat on the Ferris wheel relative to a coordinate system whose origin is at the low point of the wheel. Assume the seat begins moving at the origin.

Questions & Answers

QUESTION:

Find parametric equations that describe the circular path of the following objects. Assume (x, y) denotes the position of the object relative to the origin at the center of the circle. Use the units of time specified in the problem. There is more than one way to describe any circle.

A Ferris wheel has a radius of 20 m and completes a revolution in the clockwise direction at constant speed in 3 min. Assume that x and y measure the horizontal and vertical positions of a seat on the Ferris wheel relative to a coordinate system whose origin is at the low point of the wheel. Assume the seat begins moving at the origin.

ANSWER:

Solution 26E

Step 1:

The given ferris wheel is :

The given ferris wheel has center at $(0,20)$ since the low point is at the origin. .

The wheel completes a revolution in clockwise direction in 3 min. Using this we can find the angular velocity $\omega{}=\frac{2\Pi{}r}{t}$ .
Hence the $\omega{}=\frac{-2\Pi{}*20}{3*60\ }=\frac{-2\Pi{}}{9}rad/sec$ . (Since ferris wheel is rotating clockwise)

As we know the angular velocity , we can find position of a point on ferris wheel after time t as $\theta{}=\omega{}t=\frac{-2\Pi{}t}{9}rad/sec$ .

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