A postal employee drives a delivery truck along the route shown in figure below. Determine the magnitude and direction of the resultant by drawing scale diagram and component method

To solve this problem, let's break it down step by step using the **component method**. The key steps are:

1. **Analyze the Problem**: We'll need the route information (distances and angles) from the figure, but since I don't have access to the image, I’ll walk you through how to handle this kind of problem generally.

2. **Decompose the Directions**: The delivery truck might follow paths in multiple directions. For example, a route might be divided into segments (north, east, south, west, or at angles). You break down each segment into **horizontal (x) and vertical (y)** components.

3. **Add the Components**: Once each segment has been decomposed into \( x \) and \( y \) components, you sum them up to find the net displacement along each axis.

4. **Find the Resultant**: The magnitude of the resultant vector is given by \( R = \sqrt{(R_x^2 + R_y^2)} \), where \( R_x \) and \( R_y \) are the sum of the horizontal and vertical components.

5. **Determine the Direction**: The direction (angle) of the resultant vector can be found using the formula \( \theta = \tan^{-1} \left( \frac{R_y}{R_x} \right) \).

If you can upload the image of the route or give the details about the angles and distances involved, I can guide you through the exact numbers. Alternatively, you could also draw a **scale diagram** on paper using a protractor and ruler, representing each segment as a vector, and then measure the resultant vector’s magnitude and direction directly.

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If you have any details to share or a picture to upload, feel free to provide it. In the meantime, here are some related questions:

1. How would you break a vector at 30 degrees to the horizontal into components?
2. What happens to the resultant vector when two displacement vectors are added in opposite directions?
3. Can the magnitude of the resultant vector ever be less than the magnitude of any of the individual vectors? 
4. How do vector diagrams differ from scalar diagrams in representing physical quantities?
5. What role does the Pythagorean theorem play in calculating resultant magnitudes?

**Tip**: Always use the proper units (e.g., meters, kilometers) in both the calculation and the final answer to ensure consistency.

A postal employee drives a delivery truck along the route shown in figure below. Determine the magnitude and direction of the resultant by drawing scale diagram and component method.

Learn how to determine the magnitude and direction of the resultant vector for a postal truck route using vector decomposition and the component method. This detailed explanation covers vector addition, the Pythagorean theorem, and key trigonometric concepts. Suitable for students in Grades 9-12.

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