One night after escaping Jurassic Park, Fluffy and Talula are accidentally awoken by a ranger in an attempt to recapture them. Fluffy runs off at S69°E at 40 mph while Talula heads S11°W. After 15 mins, the velociraptors have escaped. If the bearing from Talula to Fluffy is N43°E, how far apart are they?
One night after escaping Jurassic Park, Fluffy and Talula are accidentally awoken by a ranger in an attempt to recapture them. Fluffy runs off at S69°E at 40 mph while Talula heads S11°W. After 15 mins, the velociraptors have escaped. If the bearing from Talula to Fluffy is N43°E, how far apart are they?
Chapter2: Loads On Structures
Section: Chapter Questions
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Transcribed Image Text:Below you will find a detailed transcription of the data table suitable for an educational website. The table appears to show a variety of numerical data, including directional coordinates, possibly indicating measurements related to geography, navigation, or physics.
| 176.2 | 152.7 | 23.8 | 17.5 | 2.8 |
|-------|-------|---------|---------|---------|
| 10.8 | N86.6°E | S4.5°W | N81.5°E | 16.2 |
| 11.5 | 25.3 | 18.6 | 164.0 | N57.5°W |
| 7.6 | 19.7 | 3.14 | 26.9 | 12.9 |
| S56.6°E| 18.9 | 16.9 | 5.8 | 1.6 |
**Explanation of the Table:**
- The table consists of five columns, each containing five rows of data.
- It features a mix of numerical values and directional coordinates (e.g., N86.6°E, S4.5°W).
- N and S denote North and South, respectively, while E and W denote East and West.
- The numbers associated with these coordinates likely measure angles or directions in degrees.
- The values might represent various parameters or measurements, but the exact context is not provided.
![**Problem 6: Velociraptor Escape and Bearing Calculation**
One night after escaping Jurassic Park, Fluffy and Talula are accidentally awoken by a ranger in an attempt to recapture them. Fluffy runs off at S69°E at 40 mph while Talula heads S11°W. After 15 minutes, the velociraptors have escaped. If the bearing from Talula to Fluffy is N43°E, how far apart are they?
This problem involves determining the distance between two points after the velociraptors, Fluffy and Talula, have traveled in different directions for a specified amount of time. Fluffy's path has a bearing of S69°E, and Talula's path has a bearing of S11°W. The calculation takes into account:
- The speed at which Fluffy is traveling (40 mph).
- The time taken for their escape (15 minutes or 0.25 hours).
- The bearing from Talula to Fluffy (N43°E).
### Explanation of Key Concepts:
- **Bearing:** The direction or path along which something moves or along which it lies.
- **Travel Time Conversion:** Converting minutes into hours as it's given that Fluffy's speed is in miles per hour.
### Detailed Steps for Solution:
1. **Convert travel time**:
15 minutes = 15/60 hours = 0.25 hours
2. **Calculate distance traveled by Fluffy**:
\[
\text{Distance} = \text{Speed} \times \text{Time} = 40 \, \text{mph} \times 0.25 \, \text{hours} = 10 \, \text{miles}
\]
3. **Represent paths and bearings on a coordinate system**:
- Fluffy moves S69°E, meaning 69 degrees east of due south.
- Talula moves S11°W, meaning 11 degrees west of due south.
4. **Use trigonometry and vector analysis**: To determine the relative positions and calculate the straight-line distance between them.
### Diagram and Calculation:
Given the coordinates and initial positions are detailed, you would typically use:
\[ \Delta x = x_{\text{Fluffy}} - x_{\text{Talula}} \]
\[ \Delta y = y_{\text{Fluffy}} - y_{\text{Talula}} \]
Following](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d473413-bcea-4706-8a6c-0dae0f6f8353%2F5679c435-663a-4c79-9190-d97905eb92c1%2F7ir5lvs_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 6: Velociraptor Escape and Bearing Calculation**
One night after escaping Jurassic Park, Fluffy and Talula are accidentally awoken by a ranger in an attempt to recapture them. Fluffy runs off at S69°E at 40 mph while Talula heads S11°W. After 15 minutes, the velociraptors have escaped. If the bearing from Talula to Fluffy is N43°E, how far apart are they?
This problem involves determining the distance between two points after the velociraptors, Fluffy and Talula, have traveled in different directions for a specified amount of time. Fluffy's path has a bearing of S69°E, and Talula's path has a bearing of S11°W. The calculation takes into account:
- The speed at which Fluffy is traveling (40 mph).
- The time taken for their escape (15 minutes or 0.25 hours).
- The bearing from Talula to Fluffy (N43°E).
### Explanation of Key Concepts:
- **Bearing:** The direction or path along which something moves or along which it lies.
- **Travel Time Conversion:** Converting minutes into hours as it's given that Fluffy's speed is in miles per hour.
### Detailed Steps for Solution:
1. **Convert travel time**:
15 minutes = 15/60 hours = 0.25 hours
2. **Calculate distance traveled by Fluffy**:
\[
\text{Distance} = \text{Speed} \times \text{Time} = 40 \, \text{mph} \times 0.25 \, \text{hours} = 10 \, \text{miles}
\]
3. **Represent paths and bearings on a coordinate system**:
- Fluffy moves S69°E, meaning 69 degrees east of due south.
- Talula moves S11°W, meaning 11 degrees west of due south.
4. **Use trigonometry and vector analysis**: To determine the relative positions and calculate the straight-line distance between them.
### Diagram and Calculation:
Given the coordinates and initial positions are detailed, you would typically use:
\[ \Delta x = x_{\text{Fluffy}} - x_{\text{Talula}} \]
\[ \Delta y = y_{\text{Fluffy}} - y_{\text{Talula}} \]
Following
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