**Problem Statement:**A man walks 18 km west and then 25 km south.1. Calculate his displacement magnitude.2. Calculate his displacement direction.**Solution Explanation:**To solve this problem, we need to determine the displacement, which is a vector quantity that indicates the change in position. It has both magnitude and direction.**1. Calculating Displacement Magnitude:**Displacement magnitude can be found using the Pythagorean theorem, where the legs of the right triangle are the distances walked west and south.- Westward distance = 18 km- Southward distance = 25 kmDisplacement magnitude (D) is calculated as:\[ D = \sqrt{(18 \, \text{km})^2 + (25 \, \text{km})^2} \]**2. Calculating Displacement Direction:**The displacement direction can be calculated using trigonometry, specifically by finding the angle θ using the tangent function:\[ \tan \theta = \frac{\text{southward distance}}{\text{westward distance}} = \frac{25}{18} \]The angle θ can be found using:\[ \theta = \tan^{-1} \left(\frac{25}{18}\right) \]This angle is measured from the west direction towards the south.

Given data- a man walks west =18 km south =25 km

Answered: A man walks 18 km west then 25 km…

A man walks 18 km west then 25 km south. 1. Calculate his displacement magnitude. 2. Calculate his displacement direction.

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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Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

**Problem Statement:**

A man walks 18 km west and then 25 km south.

1. Calculate his displacement magnitude.
2. Calculate his displacement direction.

**Solution Explanation:**

To solve this problem, we need to determine the displacement, which is a vector quantity that indicates the change in position. It has both magnitude and direction.

**1. Calculating Displacement Magnitude:**

Displacement magnitude can be found using the Pythagorean theorem, where the legs of the right triangle are the distances walked west and south.

- Westward distance = 18 km
- Southward distance = 25 km

Displacement magnitude (D) is calculated as:

\[ D = \sqrt{(18 \, \text{km})^2 + (25 \, \text{km})^2} \]

**2. Calculating Displacement Direction:**

The displacement direction can be calculated using trigonometry, specifically by finding the angle θ using the tangent function:

\[ \tan \theta = \frac{\text{southward distance}}{\text{westward distance}} = \frac{25}{18} \]

The angle θ can be found using:

\[ \theta = \tan^{-1} \left(\frac{25}{18}\right) \]

This angle is measured from the west direction towards the south.

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