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 the movement as two perpendicular components, where the pirate walks 39 meters east and 80 meters north. These two displacements form a right triangle, where the magnitude of the resultant displacement corresponds to the hypotenuse.

We can use the **Pythagorean theorem** to find the resultant displacement \( R \):
\[
R = \sqrt{(39^2 + 80^2)}
\]
Now, let's calculate it.

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

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

Would you like further explanation or have any questions?

Here are 5 related questions:
1. What is the direction (angle) of the resultant displacement?
2. How would the displacement change if the pirate also walked 50 meters south after his initial movements?
3. What if the pirate walked 39 meters west instead of east? How would this affect the displacement?
4. Can you calculate the total distance the pirate walked, in contrast to the resultant displacement?
5. How does the concept of vector addition apply to this problem?

**Tip:** When dealing with right triangles, the Pythagorean theorem is essential for finding the magnitude of the hypotenuse or resultant in displacement problems!

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 after walking 39 meters east and 80 meters north. This problem uses the Pythagorean theorem to solve for the hypotenuse in a right triangle, making it suitable for students in Grades 8-10.

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