Question 6 Hint 1 Hint 2 Suppose you walk 23 m straight west and then 14 m straight north. Answer all questions assuming the + x - axis is to the east. < > • How far are you from your starting point? D = m = • What is your displacement vector? Ax x + y) m • What is the direction of your displacement? 0 = degrees relative to the + x - axis.

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### Question 6

Suppose you walk 23 m straight west and then 14 m straight north. Answer all questions assuming the \( +x \) - axis is to the east.

- **How far are you from your starting point?**

\[ D = \boxed{ \ \ \ \ \ \ \ \ } \text{ m} \]

- **What is your displacement vector?**

\[ \Delta \vec{x} = (\boxed{ \ \ \ \ \ \ \ \ } \hat{x} + \boxed{ \ \ \ \ \ \ \ \ } \hat{y}) \text{ m} \]

- **What is the direction of your displacement?**

\[ \theta = \boxed{ \ \ \ \ \ \ \ \ } \text{ degrees relative to the } +x \text{ - axis.} \]

#### Hints
- [Hint 1](#)
- [Hint 2](#)

### Explanation:
In this problem, you are required to calculate the overall displacement and direction after walking a certain distance west and north from your starting point. 

The "+x" axis is to the east, which means west corresponds to the negative x-direction and north corresponds to the positive y-direction. 

1. **Distance from starting point (D)**: This can be found using the Pythagorean theorem where the legs of the right triangle are 23 m and 14 m.
   
2. **Displacement Vector (\(\Delta \vec{x}\))**: This vector is expressed in terms of its x-component and y-component. Walking west 23 m gives an x-component of -23, and walking north 14 m gives a y-component of +14. 

3. **Direction (\(\theta\))**: The direction of the vector can be found using trigonometry, specifically the arctangent function, to find the angle of the displacement vector relative to the positive x-axis.

Please replace the boxed spaces with your calculations.
Transcribed Image Text:### Question 6 Suppose you walk 23 m straight west and then 14 m straight north. Answer all questions assuming the \( +x \) - axis is to the east. - **How far are you from your starting point?** \[ D = \boxed{ \ \ \ \ \ \ \ \ } \text{ m} \] - **What is your displacement vector?** \[ \Delta \vec{x} = (\boxed{ \ \ \ \ \ \ \ \ } \hat{x} + \boxed{ \ \ \ \ \ \ \ \ } \hat{y}) \text{ m} \] - **What is the direction of your displacement?** \[ \theta = \boxed{ \ \ \ \ \ \ \ \ } \text{ degrees relative to the } +x \text{ - axis.} \] #### Hints - [Hint 1](#) - [Hint 2](#) ### Explanation: In this problem, you are required to calculate the overall displacement and direction after walking a certain distance west and north from your starting point. The "+x" axis is to the east, which means west corresponds to the negative x-direction and north corresponds to the positive y-direction. 1. **Distance from starting point (D)**: This can be found using the Pythagorean theorem where the legs of the right triangle are 23 m and 14 m. 2. **Displacement Vector (\(\Delta \vec{x}\))**: This vector is expressed in terms of its x-component and y-component. Walking west 23 m gives an x-component of -23, and walking north 14 m gives a y-component of +14. 3. **Direction (\(\theta\))**: The direction of the vector can be found using trigonometry, specifically the arctangent function, to find the angle of the displacement vector relative to the positive x-axis. Please replace the boxed spaces with your calculations.
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