Answered: If = [10 m, 30°] and = [25 m, 130°],…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section1.9: Components Of A Vector And Unit Vectors

Problem 1.8QQ: If A + B = 0, the corresponding components of the two vectors Aand Bmust be (a) equal, (b) positive,...

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If = [10 m, 30°] and = [25 m, 130°], what is the direction of the sum of these two vectors (in degrees from the positive x-axis)?

Expert Solution

Step 1

Given data

The magnitude of the vector A is given as $|A| = 10 m$ .
The direction of vector A is given as $θ_{A} = 30 °$ .
The magnitude of the vector B is given as $|B| = 25 m$ .
The direction of vector B is given as $θ_{B} = 130 °$ .

The vector equation for vector A is obtained as,

$\vec{A} = (|A| \cos θ_{A}) \hat{i} + (|A| \sin θ_{A}) \hat{j} \vec{A} = (10 \cos 30 °) \hat{i} + (10 \sin 30 °) \hat{j} \vec{A} = 8.66 \hat{i} + 5 \hat{j}$

The vector equation for vector A is obtained as,

$\vec{B} = (|B| \cos θ_{B}) \hat{i} + (|B| \sin θ_{B}) \hat{j} \vec{B} = (25 \cos 130 °) \hat{i} + (25 \sin 130 °) \hat{j} \vec{B} = - 16.07 \hat{i} + 19.15 \hat{j}$

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