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A person going for a walk follows the path shown in the figure, where y, = 302 m and 0 = 54.0°. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point? magnitude m direction ° counterclockwise from the +x axis Start 100 m End 200 m 30.0 150 m

A person going for a walk follows the path shown in the figure, where y, = 302 m and 0 = 54.0°. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point? magnitude m direction ° counterclockwise from the +x axis Start 100 m End 200 m 30.0 150 m

College Physics
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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## Problem Statement: Displacement Calculation A person going for a walk follows the path shown in the figure below. The total trip consists of four straight-line paths. The figure specifies that \( y_1 = 302 \) m and \( \theta = 54.0^\circ \). At the end of the walk, what is the person’s resultant displacement measured from the starting point? ### Parameters: - \( y_1 \) (Vertical distance): 302 m - \( \theta \) (Angle): 54.0° ### Resultant Displacement: - **Magnitude**: To be calculated - **Direction**: To be calculated (° counterclockwise from the +x axis) ### Diagram Explanation The diagram illustrates the following path segments: 1. Starting at the origin (0,0), the person walks vertically downwards a distance of 302 m, labeled as \( y_1 \). This segment is vertical along the y-axis. 2. From this point, the person walks horizontally to the right a distance of 100 m, along the x-axis. 3. The next segment of the path is an angular path where the person walks 150 m at an angle of 30.0° below the horizontal. This segment can be broken down into horizontal and vertical components. 4. Finally, the person walks 200 m straight upwards to the end point. ### Calculations Needed To find the resultant displacement, we need to calculate: 1. The horizontal component of each segment. 2. The vertical component of each segment. 3. Summing these components to get the overall displacement vector. 4. Finding the magnitude and direction of this vector. ### Steps for Calculation 1. **Vertical components**: - Initial vertical displacement: \( y_1 = 302 \) m downward. - Upward movement at the last segment: 200 m. - Effective vertical displacement: \( 302 - 200 = 102 \) m downward. 2. **Horizontal components**: - Initial horizontal displacement: 100 m to the right. - For the angular segment (150 m at 30.0° below the horizontal): - Horizontal component: \( 150 \cos(30^\circ) \) - Vertical component: \( 150 \sin(30^\circ) \) - Effective horizontal displacement: \( 100 + 150\cos(30^\
Transcribed Image Text:## Problem Statement: Displacement Calculation A person going for a walk follows the path shown in the figure below. The total trip consists of four straight-line paths. The figure specifies that \( y_1 = 302 \) m and \( \theta = 54.0^\circ \). At the end of the walk, what is the person’s resultant displacement measured from the starting point? ### Parameters: - \( y_1 \) (Vertical distance): 302 m - \( \theta \) (Angle): 54.0° ### Resultant Displacement: - **Magnitude**: To be calculated - **Direction**: To be calculated (° counterclockwise from the +x axis) ### Diagram Explanation The diagram illustrates the following path segments: 1. Starting at the origin (0,0), the person walks vertically downwards a distance of 302 m, labeled as \( y_1 \). This segment is vertical along the y-axis. 2. From this point, the person walks horizontally to the right a distance of 100 m, along the x-axis. 3. The next segment of the path is an angular path where the person walks 150 m at an angle of 30.0° below the horizontal. This segment can be broken down into horizontal and vertical components. 4. Finally, the person walks 200 m straight upwards to the end point. ### Calculations Needed To find the resultant displacement, we need to calculate: 1. The horizontal component of each segment. 2. The vertical component of each segment. 3. Summing these components to get the overall displacement vector. 4. Finding the magnitude and direction of this vector. ### Steps for Calculation 1. **Vertical components**: - Initial vertical displacement: \( y_1 = 302 \) m downward. - Upward movement at the last segment: 200 m. - Effective vertical displacement: \( 302 - 200 = 102 \) m downward. 2. **Horizontal components**: - Initial horizontal displacement: 100 m to the right. - For the angular segment (150 m at 30.0° below the horizontal): - Horizontal component: \( 150 \cos(30^\circ) \) - Vertical component: \( 150 \sin(30^\circ) \) - Effective horizontal displacement: \( 100 + 150\cos(30^\
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