If an airplane travels 16.0° north of east for 174 km, how far east and how far north did it travel? In other words, what are the magnitudes of the east component and north component of the plane's displacement?
(a) east component

(b) north component

To find the east and north components of the airplane's displacement, we can use trigonometry. Specifically, we'll use the cosine and sine functions to resolve the displacement vector into its components.

Given:
- The airplane's total displacement \( d = 174 \, \text{km} \)
- The angle \( \theta = 16.0^\circ \) north of east

### (a) East Component
The east component \( d_{\text{east}} \) is found using the cosine function:
\[
d_{\text{east}} = d \times \cos(\theta)
\]
\[
d_{\text{east}} = 174 \times \cos(16.0^\circ)
\]

### (b) North Component
The north component \( d_{\text{north}} \) is found using the sine function:
\[
d_{\text{north}} = d \times \sin(\theta)
\]
\[
d_{\text{north}} = 174 \times \sin(16.0^\circ)
\]

Now, let's calculate these values.The components of the airplane's displacement are:

(a) **East component:** approximately \( 167.26 \, \text{km} \)

(b) **North component:** approximately \( 47.96 \, \text{km} \)

Do you want more details or have any questions?

Here are some related questions:
1. How would the components change if the angle was 30° north of east?
2. What would be the components if the airplane traveled 200 km at the same angle?
3. Can we determine the airplane's final position relative to its starting point using these components?
4. How would you find the direction of the displacement vector given the components?
5. What are the east and north components if the airplane traveled 100 km directly east?

**Tip:** Understanding how to decompose vectors into components is useful for solving many problems involving directions and forces.

Learn how to calculate the east and north components of an airplane's displacement using trigonometry. Given an angle of 16.0° north of east and a total displacement of 174 km, find the magnitudes of each component. Understand the application of cosine and sine functions in resolving vector components. Suitable for students in Grades 10-12.

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