(a) Explanation Section 1 : To determine: The Cartesian coordinates of the point having polar coordinates ( 2.50 m, 30 .0 ° ) . Answer: The Cartesian coordinates of the point having polar coordinates ( 2.50 m, 30 .0 ° ) are ( 2.17 , 1.25 ) m . Explanation: Given information: The given two points have Polar coordinates ( 2.50 m, 30 .0 ° ) and ( 3.80 m, 120 .0 ° ) . Formula to calculate the x -coordinate for the first point is, x 1 = r 1 cos θ 1 x 1 is the x -coordinate of the first point. r 1 is the distance in the polar coordinates. θ 1 is the angle in the polar coordinates. Substitute 2.50 m for r 1 and 30.0 ° for θ 1 in above expression. x 1 = ( 2.50 m ) cos ( 30.0 ° ) = 2.17 m Formula to calculate the y -coordinate for the first point is, y 1 = r 1 sin θ 1 y 1 is the y -coordinate of the first point. Substitute 2.50 m for r 1 and 30.0 ° for θ 1 in above expression. y 1 = ( 2.50 m ) sin ( 30.0 ° ) = 1.25 m Conclusion: Therefore, the Cartesian coordinates of the point having polar coordinates ( 2.50 m, 30 .0 ° ) are ( 2.17 , 1.25 ) m . Section 2: To determine: The Cartesian coordinates of the point having polar coordinates ( 3 (b) To determine The distance between the two points.

Physics for Scientists and Engineers, Volume 1

9th Edition

ISBN: 9781133954156

Author: Raymond A. Serway

Publisher: CENGAGE L

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Question

Chapter 3, Problem 3.4P

(a)

To determine

The Cartesian coordinates of the two points.

(b)

To determine

The distance between the two points.

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Chapter 3 Solutions

Physics for Scientists and Engineers, Volume 1

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