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 vector S = 8120 is directed at an angle θ S = 141.9 ° , T = 1540 is directed at an angle θ T = 165.2 ° and U = 3470 is directed at an angle θ U = 296 ° . 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 . Then, the x component of the resultant vector R is, R x = S x + T x + U x = S cos θ S + T cos θ T + U cos θ U = 8120 cos 141.9 ° + 1540 cos 165.2 ° + 3470 cos 296 ° = ( − 6390 ) + ( − 1490 ) + 1520 That is, R x = − 6360 . Similarly, the y component of the resultant vector R is, R y = S y + T y + U y = S sin θ S + T sin θ T + U sin θ U = 8120 sin 141

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Author: Evans

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Chapter 9, Problem 22RE

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The Resultant vector R and standard position angle θ by adding the components S=8120,θS=141.9°,T=1540,θT=165.2° and U=3470,θU=296°.

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Chapter 9, Problem 21RE

Chapter 9, Problem 23RE

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Chapter 9 Solutions

EBK 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 and standard position angle θ by adding the components S = 8120 , θ S = 141.9 ° , T = 1540 , θ T = 165.2 ° and U = 3470 , θ U = 296 ° .

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The Resultant vector R and standard position angle θ by adding the components S=8120,θS=141.9°,T=1540,θT=165.2° and U=3470,θU=296°.

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