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The problem asks us to determine the displacement between the base camp and Camp B in a mountain climbing expedition, where the coordinates of Camp A and Camp B are given relative to the base camp.

### Information provided:
- **Camp A** is 11,200 m east and 3,200 m above the base camp.
- **Camp B** is 8,400 m east of and 1,700 m higher than Camp A.

We can break down this problem into vector components, treating it like a 2D problem with horizontal (eastward) and vertical (height) components.

### Step-by-step solution:
1. **Coordinates of Camp A (relative to base camp)**:
   - Horizontal: \( x_A = 11,200 \, \text{m} \) east
   - Vertical: \( y_A = 3,200 \, \text{m} \) above base camp

2. **Coordinates of Camp B (relative to base camp)**:
   - Camp B is \( 8,400 \, \text{m} \) east of Camp A. So, the total horizontal distance from the base camp to Camp B is:
     \[
     x_B = x_A + 8,400 = 11,200 + 8,400 = 19,600 \, \text{m} \, (\text{east of base camp})
     \]
   - Camp B is \( 1,700 \, \text{m} \) higher than Camp A. So, the total vertical distance from the base camp to Camp B is:
     \[
     y_B = y_A + 1,700 = 3,200 + 1,700 = 4,900 \, \text{m} \, (\text{above base camp})
     \]

3. **Displacement**: 
   The displacement is the straight-line distance between the base camp and Camp B, which can be calculated using the Pythagorean theorem:
   \[
   \text{Displacement} = \sqrt{(x_B^2 + y_B^2)}
   \]
   Substituting the values:
   \[
   \text{Displacement} = \sqrt{(19,600^2 + 4,900^2)} = \sqrt{(384,160,000 + 24,010,000)} = \sqrt{408,170,000}
   \]
   \[
   \text{Displacement} \approx 20,199 \, \text{m}
   \]

Thus, the displacement between the base camp and Camp B is approximately **20,199 meters**.

Would you like further details on this solution, or have any questions?

### Expanding on this:
1. What is the significance of using the Pythagorean theorem in displacement problems?
2. How would the problem change if Camp B was west of Camp A instead of east?
3. How can the concept of vectors be applied to similar real-life navigation problems?
4. Why is displacement different from distance traveled in this scenario?
5. How would the problem change if another camp, Camp C, were added further east and higher than Camp B?

#### Tip:
When dealing with 2D displacement problems, breaking down movements into horizontal and vertical components simplifies the calculation.

A mountain climbing expedition establishes a base camp and two intermediate camps, A and B. Camp A is 11,200 m east of and 3,200 m above base camp. Camp B is 8400 m east of and 1700 m higher than Camp A. Determine the displacement between base camp and Camp B.

Solve a displacement problem in a mountain climbing scenario, using vector components and the Pythagorean theorem. Camp A is 11,200 m east and 3,200 m above the base camp, while Camp B is 8,400 m east of and 1,700 m higher than Camp A. Calculate the displacement with detailed steps.

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