Physics Question is attached image **Question 37: Vector Components and Angles****Problem Statement:**The components of vector **A** are \( A_x \) and \( A_y \) (both positive), and the angle that it makes with respect to the positive x axis is \( \theta \). Find the angle \( \theta \) if the components of the displacement vector **A** are:**(a)** \( A_x = 12 \, \text{m} \) and \( A_y = 12 \, \text{m} \)**(b)** \( A_x = 17 \, \text{m} \) and \( A_y = 12 \, \text{m} \)**(c)** \( A_x = 12 \, \text{m} \) and \( A_y = 17 \, \text{m} \)**Explanation:**### Solution Overview:To find the angle \( \theta \) made with the positive x-axis, you can use the trigonometric relation involving the arctangent function:\[ \theta = \tan^{-1} \left( \frac{A_y}{A_x} \right) \]### Detailed Solutions:1. **Case (a):** Given \( A_x = 12 \, \text{m} \) and \( A_y = 12 \, \text{m} \), \[ \theta = \tan^{-1} \left( \frac{12}{12} \right) = \tan^{-1}(1) = 45^\circ \]2. **Case (b):** Given \( A_x = 17 \, \text{m} \) and \( A_y = 12 \, \text{m} \), \[ \theta = \tan^{-1} \left( \frac{12}{17} \right) \] Using a calculator or trigonometric tables to find the inverse tangent, \[ \theta \approx 35.5^\circ \]3. **Case (c):** Given \( A_x = 12 \, \text{m} \) and \( A_y = 17 \, \text{m} \), \[ \theta = \tan^{-1} \left( \frac{17}{12}

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37. Go The components of vector A are A, and A, (both positive), and the angle that it makes with respect to the positive x axis is 0. Find the angle 0 if the components of the displacement vector A are (a) A, = 12 m and A, 12 m, (b) A, = 17 m and Ay 12 m, and (c) A, A, = 17 m. = 12 m and =

37. Go The components of vector A are A, and A, (both positive), and the angle that it makes with respect to the positive x axis is 0. Find the angle 0 if the components of the displacement vector A are (a) A, = 12 m and A, 12 m, (b) A, = 17 m and Ay 12 m, and (c) A, A, = 17 m. = 12 m and =

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 2.11CYU: Check Your Understanding For the vectors given in Figure 2.13, find the scalar products AB and FC ....

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