Explanation Procedure used: To find x and y components of a vector: 1. Place the vector A such that θ is in standard position. 2. Calculate A x and A y from A x = A cos θ and A y = A sin θ . Use the reference angle if the direction of the component is noted. 3. Check the components to see if each is in the correct direction and has a magnitude that is proper for the reference angle. Adding vectors by components: 1. Add the x -component of the given vectors to obtain R x . 2. Add the y -component of the given vectors to obtain R y . 3. Find the magnitude of the resultant R . Use the equation R = R x 2 + R y 2 . 4. Find the standard-position angle θ for the resultant R . Find the reference angle θ r e f for the resultant R by using the equation θ r e f = tan − 1 | R y | | R x | . Then, use the reference angle and the quadrant of R to determine the standard position angle θ . Calculation: The given vectors A = 368 is directed at an angle θ A = 235.3 ° and B = 227 is directed at an angle θ B = 295.0 ° Sketch the figure of the corresponding vectors as shown below in Figure 1. From Figure 1, the resultant vector R will be in third quadrant. The x and y components of a vector A is, A x = A cos θ and A y = A sin θ A x = 368 cos 235.3 ° and A y = 368 sin 235.3 ° A x ≈ − 209.4948646 and A y ≈ − 302.5490071 Similarly, the x and y components of a vector B is, B x = B cos θ and B y = B sin θ B x = 227 cos 295 ° and B y = 227 sin 295 ° B x ≈ 95.93434542 and B y ≈ − 205.7318677 Then, the x component of the resultant vector R is, R x = A x + B x = 18 + 10

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 9.3, Problem 17E

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The resultant vector R and standard position angle θ by adding the components A=368,θA=235.3°,B=227 and θB=295.0°.

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Chapter 9.3, Problem 16E

Chapter 9.3, Problem 18E

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Chapter 9 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

Ch. 9.1 - For the vectors in Example 2, show that R = B + C...Ch. 9.1 - Prob. 2PE Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E

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The resultant vector R and standard position angle θ by adding the components A = 368 , θ A = 235.3 ° , B = 227 and θ B = 295.0 ° .

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The resultant vector R and standard position angle θ by adding the components A=368,θA=235.3°,B=227 and θB=295.0°.

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Chapter 9 Solutions