Halifax, Nova Scotia has a latitude of 45 N, and Buesno Aires, Argentina a latitude of 34 S. Assume that the two cities lie on the same north-south line and find the distance in kilometers between them.
The correct answer and explanation is :
To find the distance between Halifax, Nova Scotia (latitude ( 45^\circ N )) and Buenos Aires, Argentina (latitude ( 34^\circ S )), we assume both cities lie along the same north-south line, meaning we only need to calculate the difference in latitude and convert it into a physical distance.
Step 1: Find the Difference in Latitude
- Halifax: ( 45^\circ N )
- Buenos Aires: ( 34^\circ S )
- Difference in latitude = ( 45^\circ + 34^\circ = 79^\circ )
Step 2: Convert Latitude Difference into Distance
The Earth’s circumference is approximately 40,075 km along the equator. However, for meridional (north-south) distances, we use the meridional circumference of the Earth, which is about 40,008 km (since Earth is slightly oblate).
The length of one degree of latitude is:
[
\frac{40,008}{360} \approx 111.14 \text{ km per degree}
]
Thus, the total distance between Halifax and Buenos Aires is:
[
79^\circ \times 111.14 \approx 8,782 \text{ km}
]
Conclusion
The approximate north-south distance between Halifax, Nova Scotia, and Buenos Aires, Argentina, is 8,782 kilometers. This calculation assumes a perfectly spherical Earth, and actual distances may vary slightly due to Earth’s shape and terrain variations.