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 A = 22.51 is directed at an angle θ A = 130.16 ° and B = 7.604 is directed at an angle θ B = 200.09 ° . 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 A is, A x = A cos θ and A y = A sin θ A x = 22.51 cos 130.16 ° and A y = 22.51 sin 130.16 ° A x = − 14.52 and A y = 17.20 Similarly, the x and y components of a vector B is, B x = B cos θ and B y = B sin θ B x = 7.604 cos 200.09 ° and B y = 7.604 sin 200.09 ° B x = − 7.14 and B y = − 2.61 Then, the x component of the resultant vector R is, R x = A x + B x = ( − 14

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ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

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Chapter 9, Problem 17RE

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The Resultant vector R and standard position angle θ by adding the components A=22.51,θA=130.16°,B=7.604 and θB=200.09°.

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Chapter 9, Problem 16RE

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Chapter 9 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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 = 22.51 , θ A = 130.16 ° , B = 7.604 and θ B = 200.09 ° .

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The Resultant vector R and standard position angle θ by adding the components A=22.51,θA=130.16°,B=7.604 and θB=200.09°.

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