To determine The Resultant vector R and standard position angle θ by adding the components J = 0.0120 , θ J = 370.5 ° , K = 0.00781 and θ K = 260.0 ° . Explanation Procedure used: To find x andy 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 J = 0.0120 is directed at an angle θ J = 370.5 ° and K = 0.00781 is directed at an angle θ K = 260.0 ° Sketch the figure of the corresponding vectors as shown below in Figure 1. From Figure 1, it is observed that the resultant vector is represented as R . The x and y components of a vector J is, J x = J cos θ and J y = J sin θ J x = 0.0120 cos 370.5 ° and J y = 0.0120 sin 370.5 ° J x = 0.0117 and J y = 0.00218 Similarly, the x and y components of a vector K is, K x = K cos θ and K y = K sin θ K x = 0.00781 cos 260 ° and K y = 0.00781 sin 260 ° K x = − 0.001356 and K y = − 0.00769 Then, the x component of the resultant vector R is, R x = J x + K x = 0

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 9, Problem 16RE

To determine

The Resultant vector R and standard position angle θ by adding the components J=0.0120,θJ=370.5°,K=0.00781 and θK=260.0°.

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Chapter 9, Problem 15RE

Chapter 9, Problem 17RE

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Chapter 9 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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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