   Chapter 1, Problem 43P

Chapter
Section
Textbook Problem

Two points are given in polar coordinates by (r, θ) = (2.00 m, 50.0°) and (r, θ) = (5.00 m, −50.0°), respectively. What is the distance between them?

To determine
The distance between two points.

Explanation

Given Info: The polar coordinate of a point is (r1,θ1)=(2.0m,50°) and the polar coordinate of the another point is (r2,θ2)=(5.0m,50°) .

Explanation:

To determine the x and y coordinate of the two points.

Formula for the Cartesian coordinate of the first point

x1=r1cosθ1

y1=r1sinθ1

Substitute 2m for r1 and 50° for θ1 , to calculate x1andy1 .

x1=(2m)(cos(50°))=1.29m

y1=(2m)(sin(50°))=1.53m

Formula for the Cartesian coordinate of the second point

x2=r2cosθ2

y2=r2sinθ2

Substitute 5m for r2 and (50°) for θ2 , to calculate x2andy2 .

x2=(5m)(cos(50°))=3.21m

y2=(5m)(sin(50°))=3.83m

Thus, the x and y coordinate of the two points are (x1,y1)=(1

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