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 = 1200 is directed at an angle θ A = 90 ° and B = 1750 is directed at an angle θ B = 115 ° Sketch the figure of the corresponding vectors as shown below in Figure 1. From Figure 1, it is observed that the vector A = 1200 is directed at an angle θ A = 90 ° and B = 1750 is directed at an angle θ B = 115 ° . Let the resultant vector be represented as R . The x and y components of the vector A are, A x = A cos θ and A y = A sin θ A x = 1200 cos 90 ° and A y = 1200 sin 90 ° A x = 0 and A y = 1200 Similarly, the x and y components of the vector B are, B x = B cos θ and B y = B sin θ B x = 1750 cos 115 ° and B y = 1750 sin 115 ° B x ≈ − 739.58 and B y ≈ 1586 Then, the x component of the resultant vector R is, R x = A x + B x = 0 + ( − 739

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 9.3, Problem 1PE

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The resultant vector R if θA is changed to 90° in Example 2.

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Chapter 9 Solutions

Basic Technical Mathematics

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 if θ A is changed to 90 ° in Example 2.

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