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The image contains a math problem written in Chinese, along with a diagram.

Here's a translation and breakdown of the problem:

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**Translation of the Problem:**

11. A car travels 9 km due south, then 5 km due east.  
(a) Calculate the total distance the car travels.  
(b) Calculate the car's displacement (distance from its starting point).  
(c) Determine the bearing of the car's final position relative to its starting point. Assume the north direction is 0 degrees.

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### Solution:

#### (a) Total Distance Traveled
The total distance the car travels is the sum of the individual distances:

\[
\text{Total Distance} = 9 \, \text{km} + 5 \, \text{km} = 14 \, \text{km}
\]

#### (b) Displacement
The displacement is the straight-line distance from the starting point to the final point. This can be calculated using the Pythagorean theorem:

\[
\text{Displacement} = \sqrt{(9 \, \text{km})^2 + (5 \, \text{km})^2}
\]

Calculating:

\[
\text{Displacement} = \sqrt{81 + 25} = \sqrt{106} \approx 10.3 \, \text{km}
\]

#### (c) Bearing of the Final Position
The bearing is calculated from the north direction. Here, we need to find the angle from the north direction to the line of displacement.

Let \(\theta\) be the angle the displacement makes with the east-west line. We can use the tangent function:

\[
\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{5}{9}
\]

\[
\theta = \tan^{-1}\left(\frac{5}{9}\right) \approx 29.05^\circ
\]

Since the car travels south and then east, its final bearing from the north is:

\[
\text{Bearing} = 180^\circ - 29.05^\circ = 150.95^\circ \, \text{(rounded to } 151^\circ\text{)}
\]

### Summary of Answers:
1. Total distance traveled: **14 km**
2. Displacement: **10.3 km**
3. Bearing from north: **151°**

Would you like further details or explanations? Here are some related questions to explore:

1. How is the Pythagorean theorem used to calculate displacement?
2. What is the difference between distance and displacement?
3. How are bearings used in navigation?
4. Can displacement ever be greater than distance?
5. How can trigonometric functions help in solving real-world problems?

**Tip:** Remember, displacement is always the shortest path between two points, while distance is the total path traveled!

A car travels 9 km south, then 5 km east. Calculate the total distance, displacement, and bearing of the final position relative to the starting point.

Solve a real-world problem involving a car traveling south and east. Learn how to calculate the total distance (14 km), displacement (10.3 km), and bearing (151°) using the Pythagorean theorem and trigonometry. Suitable for students in Grades 8-10.

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