https://file.aiquickdraw.com/mathbot/file/1738949472854fl744wz8.jpg

This problem involves determining the magnitude of the displacement vector for the aircraft traveling from point \( A \) to point \( C \), via \( B \), using the given displacement triangle. 

### Solution:

1. **Triangle Setup**:
   - From the diagram:
     - \( AB = 360 \, \text{km} \) (southward),
     - \( BC = 100 \, \text{km} \) (eastward).

2. **Displacement Vector \( AC \)**:
   The total displacement from \( A \) to \( C \) forms the hypotenuse of a right triangle where:
   - The southward displacement (\( AB \)) is one leg of the triangle.
   - The eastward displacement (\( BC \)) is the other leg.

   Using the Pythagorean theorem:
   \[
   AC = \sqrt{AB^2 + BC^2}
   \]
   Substitute the values:
   \[
   AC = \sqrt{(360)^2 + (100)^2}
   \]
   \[
   AC = \sqrt{129600 + 10000}
   \]
   \[
   AC = \sqrt{139600}
   \]
   \[
   AC = 374 \, \text{km} \, (\text{approx. to nearest whole number}).
   \]

### Final Answer:
The magnitude of the displacement from \( A \) to \( C \) is **374 km**.

---

Would you like a deeper explanation or have other questions? 😊  

### Related Questions:
1. What is the direction (angle) of the displacement vector \( AC \)?
2. How can the vector \( AC \) be represented in component form?
3. What would happen to the displacement if \( BC \) were doubled?
4. How does the Pythagorean theorem work in this context?
5. What is the significance of displacement vs. total distance traveled?

### Tip:
For problems involving displacement in two dimensions, always identify if the triangle is right-angled so you can apply the Pythagorean theorem.

Use the displacement triangle to determine the magnitude of the displacement in km of the aircraft at C from A.

Learn how to calculate the displacement of an aircraft traveling from point A to C via B using a displacement triangle. Apply the Pythagorean theorem to find the magnitude of the displacement vector with given distances of 360 km southward and 100 km eastward. Suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation