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 legs of a right triangle. The total displacement is the hypotenuse of this right triangle.

Using the Pythagorean theorem:
\[
\text{Displacement} = \sqrt{(\text{east movement})^2 + (\text{north movement})^2}
\]

Substituting the values:
\[
\text{Displacement} = \sqrt{(39)^2 + (80)^2} = \sqrt{1521 + 6400} = \sqrt{7921}
\]
\[
\text{Displacement} = 89 \, \text{m}
\]

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

Would you like further details or have any questions?

Here are 5 related questions to think about:
1. What would the direction of the pirate's displacement be relative to the east direction?
2. How would the displacement change if the pirate walked 50 m east instead of 39 m?
3. Can you express the displacement using vector notation?
4. If the pirate walked 80 m west and 39 m north, what would his displacement be?
5. How could you calculate the angle of the resultant displacement?

**Tip:** Always double-check if a problem involving movement can be solved with simple geometry, such as using the Pythagorean theorem.

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 pirate's resultant displacement after walking 39 meters east and 80 meters north using the Pythagorean theorem. This step-by-step solution explains how to apply basic geometry to find the total displacement, which is 89 meters. Suitable for students in Grades 6-8.

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