Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point? What is the direction of your displacement? Assume the +x axis is to the east.

### Part 1: How far are you from your starting point?

This is a classic problem involving displacement, where we can calculate the distance using the Pythagorean theorem. The movement west and north forms a right triangle, where:
- One leg is the distance walked west: \( 18.0 \, \text{m} \)
- The other leg is the distance walked north: \( 25.0 \, \text{m} \)

The straight-line distance \( d \) from the starting point is the hypotenuse of the right triangle:

\[
d = \sqrt{(18.0 \, \text{m})^2 + (25.0 \, \text{m})^2}
\]

\[
d = \sqrt{(324.0 + 625.0)} = \sqrt{949.0} \approx 30.8 \, \text{m}
\]

So, the distance from the starting point is approximately **30.8 meters**.

---

### Part 2: What is the direction of your displacement?

To find the direction, we need to determine the angle \( \theta \) of the displacement vector relative to the +x-axis (east direction). Since the walk was first west and then north, the angle is measured counterclockwise from the west axis. The tangent of the angle is given by:

\[
\tan \theta = \frac{\text{northward displacement}}{\text{westward displacement}} = \frac{25.0}{18.0}
\]

\[
\theta = \tan^{-1} \left( \frac{25.0}{18.0} \right) \approx \tan^{-1}(1.39) \approx 54.4^\circ
\]

Since the displacement is to the northwest, the angle is **54.4° north of west**.

---

### Summary:
- **Distance from the starting point**: \( 30.8 \, \text{m} \)
- **Direction of displacement**: \( 54.4^\circ \, \text{north of west} \)

Would you like more details or have any questions about this?  
Here are 5 related questions:
1. How would you calculate displacement if the movement was in three dimensions?
2. What is the significance of displacement in physics compared to distance?
3. How would the solution change if the movement was southeast and north instead of west and north?
4. What other trigonometric functions are commonly used to solve vector problems like this?
5. How could you use vector components to calculate the direction more easily?

**Tip:** For displacement problems, always keep track of both magnitude and direction to describe the movement accurately.

Solve a vector displacement problem where you walk 18.0 m west and 25.0 m north. Learn how to calculate the total displacement using the Pythagorean theorem and determine the angle of the direction using trigonometry. Suitable for Grades 9-12.

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