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 magnitude of the pirate's resultant displacement, we can treat his movements east and north as the two legs of a right triangle. The displacement will be the hypotenuse of this triangle.

The formula for the magnitude of the resultant displacement \( d \) is given by the Pythagorean theorem:

\[
d = \sqrt{(39^2 + 80^2)}
\]

Now let's calculate it:

\[
d = \sqrt{(39^2 + 80^2)} = \sqrt{(1521 + 6400)} = \sqrt{7921} = 89 \text{ m}
\]

Thus, the magnitude of the pirate's resultant displacement is 89 meters.

Would you like more details on how this calculation works?

Here are 5 follow-up questions:
1. What would happen if the pirate walked west instead of east?
2. How do you calculate displacement if the pirate changes direction halfway through?
3. What if the pirate’s map included a vertical descent or ascent—how would that affect displacement?
4. Can the displacement ever be larger than the total distance traveled?
5. How does the concept of displacement differ from distance in physics?

**Tip:** Displacement measures the shortest path between two points, while distance measures the total path taken, regardless of direction.

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?

Learn how to calculate the magnitude of a pirate's resultant displacement using the Pythagorean theorem. Given movements of 39 m east and 80 m north, this problem covers key concepts like displacement and geometry. Suitable for students in Grades 6-8.

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