**Problem Statement:**A truck travels 10.5 km in a direction 37.9° north of west. What is the x-component of its displacement in meters? Consider the east direction to be the positive x-direction and north to be the positive y-direction.Round your answer to 0 decimal places.**Solution Explanation:**1. **Understanding Directions:** - The truck's travel direction is 37.9° north of west. - This means we need to analyze the movement in a coordinate system where: - East is the positive x-direction. - North is the positive y-direction. 2. **Displacement Components:** - The total distance traveled by the truck is 10.5 km. - We need to find the x-component (west-east direction) of this displacement.3. **Using Trigonometry:** - To determine the x-component, we use the cosine function. - x-component = Total Distance * cos(angle) - Here, the angle is referenced from west (+180°), so we'll use angle = 180° - 37.9° = 142.1°4. **Calculating the X-Component:** - Convert 10.5 km to meters: \(10.5 \text{ km} \times 1000 \text{ m/km} = 10500 \text{ m}\) - x-component = \( 10500 \text{ m} \times \cos(142.1°) \)5. **Computing the Value:** - Using a calculator: \( \cos(142.1°) \approx -0.7547\) - x-component = \( 10500 \times -0.7547 \approx -7924.35 \text{ m} \)6. **Rounding the Answer:** - Rounded answer to 0 decimal places: -7924 m**Answer:**The x-component of the truck's displacement is -7924 meters.

Given : magnitude of displacement, S = 10.5 km = 10500 m direction : 37.9° north of…

A truck travels 10.5 km in direction 37.9° north of west. What is the x-component of its displacement in meters. Consider the east direction fo be the positive x-direction and north to be the positive y-direction.

A truck travels 10.5 km in direction 37.9° north of west. What is the x-component of its displacement in meters. Consider the east direction fo be the positive x-direction and north to be the positive y-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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Concept explainers

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 truck travels 10.5 km in a direction 37.9° north of west. What is the x-component of its displacement in meters? Consider the east direction to be the positive x-direction and north to be the positive y-direction.

Round your answer to 0 decimal places.

**Solution Explanation:**

1. **Understanding Directions:**
- The truck's travel direction is 37.9° north of west.
- This means we need to analyze the movement in a coordinate system where:
- East is the positive x-direction.
- North is the positive y-direction.

2. **Displacement Components:**
- The total distance traveled by the truck is 10.5 km.
- We need to find the x-component (west-east direction) of this displacement.

3. **Using Trigonometry:**
- To determine the x-component, we use the cosine function.
- x-component = Total Distance * cos(angle)
- Here, the angle is referenced from west (+180°), so we'll use angle = 180° - 37.9° = 142.1°

4. **Calculating the X-Component:**
- Convert 10.5 km to meters: \(10.5 \text{ km} \times 1000 \text{ m/km} = 10500 \text{ m}\)
- x-component = \( 10500 \text{ m} \times \cos(142.1°) \)

5. **Computing the Value:**
- Using a calculator:
\( \cos(142.1°) \approx -0.7547\)
- x-component = \( 10500 \times -0.7547 \approx -7924.35 \text{ m} \)

6. **Rounding the Answer:**
- Rounded answer to 0 decimal places: -7924 m

**Answer:**

The x-component of the truck's displacement is -7924 meters.

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