College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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**Problem: Vector Analysis**

A person walks at a rate of 3.10 m/s, 40.0° south of west.

(a) **Sketch a drawing showing this vector.**

(b) **Determine the components of this vector in each direction.**

(c) **How long would it take to travel 50.0 meters south?**

(d) **How far would that person have traveled west in that same amount of time?**

**Explanation for Diagrams:**

Since there are no diagrams present in the image, we will focus on explaining the vector components.

1. **Vector Direction:**
   - The vector forms an angle of 40.0° with the westward direction, directed south of west.

2. **Component Calculation:**
   - The velocity vector can be broken into two components: 
     - Westward (x-component)
     - Southward (y-component)
   - Use trigonometric functions to determine these components.
     - \( V_x = 3.10 \, \text{m/s} \times \cos(40.0^\circ) \)
     - \( V_y = 3.10 \, \text{m/s} \times \sin(40.0^\circ) \)

3. **Time Calculation for Part (c):**
   - Determine the time taken to travel 50.0 meters south using the southward velocity component:
     - \( t = \frac{50.0 \, \text{m}}{V_y} \)

4. **Distance Calculation for Part (d):**
   - Calculate the westward distance traveled in the same time period:
     - \( \text{Distance west} = V_x \times t \) 

This approach gives a comprehensive understanding of vector analysis and calculations.
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Transcribed Image Text:**Problem: Vector Analysis** A person walks at a rate of 3.10 m/s, 40.0° south of west. (a) **Sketch a drawing showing this vector.** (b) **Determine the components of this vector in each direction.** (c) **How long would it take to travel 50.0 meters south?** (d) **How far would that person have traveled west in that same amount of time?** **Explanation for Diagrams:** Since there are no diagrams present in the image, we will focus on explaining the vector components. 1. **Vector Direction:** - The vector forms an angle of 40.0° with the westward direction, directed south of west. 2. **Component Calculation:** - The velocity vector can be broken into two components: - Westward (x-component) - Southward (y-component) - Use trigonometric functions to determine these components. - \( V_x = 3.10 \, \text{m/s} \times \cos(40.0^\circ) \) - \( V_y = 3.10 \, \text{m/s} \times \sin(40.0^\circ) \) 3. **Time Calculation for Part (c):** - Determine the time taken to travel 50.0 meters south using the southward velocity component: - \( t = \frac{50.0 \, \text{m}}{V_y} \) 4. **Distance Calculation for Part (d):** - Calculate the westward distance traveled in the same time period: - \( \text{Distance west} = V_x \times t \) This approach gives a comprehensive understanding of vector analysis and calculations.
Expert Solution
Check Mark
Step 1

Given that,

the magnitude of the velocity of the person is u=3.1m/s

And he moving in 40o south of west

 

a) and then a vector diagram for the motion of man will be

Physics homework question answer, step 1, image 1

where θ=40o

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