MV German Sky steams 090° T from position 31° 21’ 
00” S 023° 13’ 00” W. Calculate the arrival position of 
MV German Sky if she steams 281 miles. 

To calculate the arrival position of MV German Sky after steaming 281 miles on a course of 090° T (true), we can follow these steps:

1. **Convert the distance into degrees**: 
   - The Earth’s circumference is approximately 24,901 miles.
   - One degree of latitude is approximately 69 miles.
   - Thus, the distance in degrees can be calculated using:
     \[
     \text{Distance in degrees} = \frac{281 \text{ miles}}{69 \text{ miles/degree}} \approx 4.07 \text{ degrees}
     \]

2. **Determine the new position**:
   - Since the course is 090° T, MV German Sky will move directly eastward. This affects only the longitude, not the latitude.
   - The starting position is 31° 21’ 00” S, 023° 13’ 00” W.

3. **Calculate the new longitude**:
   - To convert the distance into a change in longitude, we need to know that at 31° S, the length of one degree of longitude is approximately:
     \[
     \text{Length of one degree of longitude} = 69 \cos(\text{latitude}) \approx 69 \cos(31°) \approx 69 \times 0.8572 \approx 59.2 \text{ miles}
     \]
   - Therefore, one degree of longitude at this latitude is about 59.2 miles. The change in longitude will be:
     \[
     \text{Change in longitude in degrees} = \frac{281 \text{ miles}}{59.2 \text{ miles/degree}} \approx 4.75 \text{ degrees}
     \]
   - Since we are moving eastward (from W to E), the new longitude is:
     \[
     023° 13’ 00” W - 4.75° \approx 018° 27’ 00” W
     \]

4. **Final position**:
   - The latitude remains the same: 31° 21’ 00” S.
   - The new longitude is approximately 018° 27’ 00” W.

### Arrival Position
The arrival position of MV German Sky is:
**31° 21’ 00” S, 018° 27’ 00” W.**

Would you like more details on any specific part of this calculation, or do you have any questions? Here are some related questions to consider:

1. How does latitude affect the length of a degree of longitude?
2. What is the significance of true heading in navigation?
3. How would this calculation change if the course was to the northwest instead of due east?
4. What tools or methods can be used for real-time navigation adjustments at sea?
5. How do currents and wind factors affect the actual path taken during steaming?

**Tip**: When navigating, always consider external factors like currents and wind that may affect your course and speed.

MV German Sky steams 090° T from position 31° 21’ 00” S 023° 13’ 00” W. Calculate the arrival position of MV German Sky if she steams 281 miles.

Determine the arrival position of MV German Sky as it steams east from 31° 21’ 00” S 023° 13’ 00” W on a 090° T heading over a distance of 281 miles. This problem involves concepts of navigation, spherical geometry, and trigonometry, with detailed calculations for changes in latitude and longitude.

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