### Educational Content: Vectors and Their Magnitudes**Problem Statement:**If \( \mathbf{C} = [10 \, \text{m}, 30^\circ] \) and \( \mathbf{D} = [25 \, \text{m}, 130^\circ] \), what is the magnitude of the sum of these two vectors? (\(\mathbf{C}\) and \(\mathbf{D}\) are vectors)**Options:**- \( \, \, \circ \) 20 m - \( \, \, \circ \) 35 m - \( \, \, \circ \) 25 m - \( \, \, \circ \) 15 m **Explanation:**To find the magnitude of the sum of two vectors \(\mathbf{C}\) and \(\mathbf{D}\), we first need to decompose each vector into its horizontal and vertical components. Then, we add the corresponding components together and calculate the resultant vector's magnitude.1. **Decompose the vectors:** - For vector \(\mathbf{C}\): \[ \text{Horizontal Component} = 10 \, \text{m} \cdot \cos(30^\circ) \] \[ \text{Vertical Component} = 10 \, \text{m} \cdot \sin(30^\circ) \] - For vector \(\mathbf{D}\): \[ \text{Horizontal Component} = 25 \, \text{m} \cdot \cos(130^\circ) \] \[ \text{Vertical Component} = 25 \, \text{m} \cdot \sin(130^\circ) \]2. **Add the components:** - Sum of horizontal components: \[ \text{Horizontal Sum} = (10 \, \text{m} \cdot \cos(30^\circ)) + (25 \, \text{m} \cdot \cos(130^\circ)) \] - Sum of vertical components: \[ \text{Vertical Sum} = (10 \, \text{m} \cdot \sin(30^\circ)) + (25 \, \text{m} \cdot \sin(130^\

The sum of vectors C and D is calculated as shown below. C+D=10 mcosθi^+10 msinθj^+25 mcosθi^+25…

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

If C = [10 m, 30°] and D = [25 m, 130°], what is the magnitude of the sum of these two vectors? (C and D are vectors) %3D 20 m 35 m 25 m 15 m

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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