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 model his movement as a right triangle, where:

- One leg represents his walk east (39 m),
- The other leg represents his walk north (80 m).

We can use the **Pythagorean theorem** to find the magnitude of the displacement (which is the hypotenuse \( d \) of the triangle):

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

Now let's calculate it:

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

So, the magnitude of his resultant displacement is **89 meters**.

Would you like a breakdown of how the Pythagorean theorem works or more details on vectors?

Here are 5 related questions:
1. How do you calculate the direction of the displacement?
2. What is the difference between displacement and distance traveled?
3. How would this change if the pirate walked in a different direction?
4. How would adding vertical displacement affect the magnitude calculation?
5. How is displacement used in navigation or GPS?

**Tip:** Always consider both the magnitude and direction when dealing with displacement in physics.

Find out how to calculate the pirate's resultant displacement when he walks 39 meters east and 80 meters north using the Pythagorean theorem. This detailed solution includes key geometry and vector concepts, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation