The image contains a diagram and a list of angle options related to vector directions.**Diagram Explanation:**- There are three vectors labeled as \( \vec{A} \), \( \vec{B} \), and \( \vec{C} \).- The vectors originate from a common point, with coordinate axes marked as \(-x\) and \(-y\).- \( \vec{A} \) makes an angle \(\alpha\) with the \(-x\) axis.- \( \vec{B} \) makes an angle \(\beta\) with the \(-x\) axis.- \( \vec{C} \) is pointing directly downward along the \(-y\) direction.**Angle Options:**- \( \theta_R = 185^\circ \)- \( \theta_R = 257^\circ \)- \( \theta_R = 174^\circ \)- \( \theta_R = 344^\circ \)- \( \theta_R = 67.9^\circ \)- \( \theta_R = 270^\circ \) **Displacement and Direction in Vector Analysis**A student on a treasure hunt undergoes three displacements in search of the treasure, as shown below. The displacements' magnitudes and angles are:- **A** = 14.9 m, **α** = 15.0°- **B** = 16.5 m, **β** = 58.0°- **C** = 42.5 m, angle as shown in diagram**Question**: What is the direction angle θ_R of the resultant vector? Give the angle as measured counterclockwise from the +x axis. (Consider the vector components)**Diagram Explanation**:The diagram shows the three vectors on a 2D plane with an x and y axis:- Vector **A** is positioned in the second quadrant, forming an angle α with the -x axis, indicating a displacement at 15.0° relative to the negative horizontal direction.- Vector **B** is in the first quadrant, forming an angle β with the +x axis, indicating a displacement at 58.0° relative to the positive horizontal direction.- Vector **C** is oriented vertically downward along the -y axis in the fourth quadrant, with its angle indicated relative to the +x axis.The task is to determine the resultant angle θ_R of these combined displacements as measured counterclockwise from the +x axis.

Answered: Image /qna-images/answer/5007b191-aaf8-4d96-80aa-e274fb8d839d.jpg

A student on a treasure hunt undergoes three displacements in search of the treasure, as shown below. The displacements magnitudes and angles are: A = 14.9 m, a = 15.0° B = 16.5 m, B = 58.0° C= 42.5 m, angle as shown in diagram What is the direction angle OR of the resultant vector? Give the angle as measured counterclockwise from +x axis. (Consider the vector components}

A student on a treasure hunt undergoes three displacements in search of the treasure, as shown below. The displacements magnitudes and angles are: A = 14.9 m, a = 15.0° B = 16.5 m, B = 58.0° C= 42.5 m, angle as shown in diagram What is the direction angle OR of the resultant vector? Give the angle as measured counterclockwise from +x axis. (Consider the vector components}

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

The image contains a diagram and a list of angle options related to vector directions.

**Diagram Explanation:**
- There are three vectors labeled as \( \vec{A} \), \( \vec{B} \), and \( \vec{C} \).
- The vectors originate from a common point, with coordinate axes marked as \(-x\) and \(-y\).
- \( \vec{A} \) makes an angle \(\alpha\) with the \(-x\) axis.
- \( \vec{B} \) makes an angle \(\beta\) with the \(-x\) axis.
- \( \vec{C} \) is pointing directly downward along the \(-y\) direction.

**Angle Options:**
- \( \theta_R = 185^\circ \)
- \( \theta_R = 257^\circ \)
- \( \theta_R = 174^\circ \)
- \( \theta_R = 344^\circ \)
- \( \theta_R = 67.9^\circ \)
- \( \theta_R = 270^\circ \)

**Displacement and Direction in Vector Analysis**

A student on a treasure hunt undergoes three displacements in search of the treasure, as shown below. The displacements' magnitudes and angles are:

- **A** = 14.9 m, **α** = 15.0°
- **B** = 16.5 m, **β** = 58.0°
- **C** = 42.5 m, angle as shown in diagram

**Question**: What is the direction angle θ_R of the resultant vector? Give the angle as measured counterclockwise from the +x axis. (Consider the vector components)

**Diagram Explanation**:

The diagram shows the three vectors on a 2D plane with an x and y axis:

- Vector **A** is positioned in the second quadrant, forming an angle α with the -x axis, indicating a displacement at 15.0° relative to the negative horizontal direction.
- Vector **B** is in the first quadrant, forming an angle β with the +x axis, indicating a displacement at 58.0° relative to the positive horizontal direction.
- Vector **C** is oriented vertically downward along the -y axis in the fourth quadrant, with its angle indicated relative to the +x axis.

The task is to determine the resultant angle θ_R of these combined displacements as measured counterclockwise from the +x axis.

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