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

The pirate's displacement can be found by treating the problem as a right triangle, where the legs represent the distance walked east and north. The magnitude of the resultant displacement is the hypotenuse of this triangle, which can be calculated using the Pythagorean theorem:

\[
\text{Magnitude of displacement} = \sqrt{(\text{Eastward displacement})^2 + (\text{Northward displacement})^2}
\]

Substitute the values:

\[
\text{Magnitude of displacement} = \sqrt{(39)^2 + (80)^2}
\]

\[
= \sqrt{1521 + 6400}
\]

\[
= \sqrt{7921}
\]

\[
= 89 \, \text{m}
\]

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

Would you like further details or have any questions? Here are some related questions you might find useful:

1. What is the direction (angle) of the resultant displacement?
2. How would the displacement change if the pirate walked in a southwest direction instead?
3. What is the difference between displacement and distance traveled?
4. How can we calculate the angle of the resultant vector with respect to the east direction?
5. How would the solution differ if the pirate followed a curved path?

**Tip:** When solving for displacement, always remember that distance is scalar (just the total path), while displacement is a vector that considers both magnitude and 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?

Discover how to find the resultant displacement when a pirate walks 39 m east and 80 m north, using the Pythagorean theorem. This geometry problem is ideal for students in Grades 6-8 and explains the step-by-step solution with relevant formulas.

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