A pirate is trying to find his treasure based on a map he drew. He walks 39 m east and 80 m north. What is the magnitude of his resultant displacement?

To find the pirate's resultant displacement, we can treat his movements as a right triangle where:

- The horizontal distance (east) is 39 m.
- The vertical distance (north) is 80 m.

We use the Pythagorean theorem to calculate the magnitude of the displacement:

\[
\text{Resultant Displacement} = \sqrt{(39^2 + 80^2)}
\]

Let me compute that for you.The magnitude of the pirate's resultant displacement is 89 meters.

Would you like more details on the solution, or have any questions?

Here are 5 related questions for practice:
1. What would the displacement be if the pirate walked 50 m east and 100 m north?
2. How does the displacement change if the pirate walked only west and south?
3. Can you calculate the angle of the displacement relative to the eastward direction?
4. What would the displacement be if the pirate moved in a diagonal direction instead?
5. How would the result change if the pirate walked in a circular path instead of straight lines?

**Tip:** The Pythagorean theorem is a powerful tool whenever you encounter right-angled triangles in physics and geometry.

Discover how to calculate the magnitude of a pirate's resultant displacement using the Pythagorean theorem. The pirate walks 39 meters east and 80 meters north. A detailed step-by-step solution for students in Grades 8-10.

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