To determine The resultant vector R and standard position angle θ by adding the components F = 154 , θ F = 90.0 ° , T = 128 and θ T = 43.0 ° . 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, F = 154 is directed at an angle θ F = 90.0 ° and T = 128 is directed at an angle θ T = 43.0 ° . 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 F is, F x = F cos θ and F y = F sin θ F x = 154 cos 90 ° and F y = 154 sin 90 ° F x = 0 and F y = 154 Similarly, the x and y components of a vector T is, T x = T cos θ and T y = T sin θ T x = 128 cos 43 ° and T y = 128 sin 43 ° T x ≈ 93.61 and T y ≈ 87.29 Then, the x component of the resultant vector R is, R x = F x + T x = 0 + 93

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Chapter 9.3, Problem 16E

To determine

The resultant vector R and standard position angle θ by adding the components F=154,θF=90.0°,T=128 and θT=43.0°.

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Chapter 9.3, Problem 15E

Chapter 9.3, Problem 17E

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Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For 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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