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salantis
9 days ago
11

Acapulco, Mexico and Hyderabad, India both lie at 17° north latitude, and lie very nearly halfway around the world from each oth

er in an east-west direction. The radius of Earth at a latitude of 17° is about 3790 miles. Suppose that you could fly from Acapulco directly west to Hyderabad or fly directly north to Hyderabad. Which way would be shorter, and by how much? Use 3960 miles for Earth’s radius. (Hint: To fly directly north, you would go from 17° north latitude to 90° north latitude, and then back down to 17° north latitude.)
Mathematics
1 answer:
lawyer [12.1K]9 days ago
6 0
To analyze this problem, we can treat the Earth as a sphere. For circular arcs, the arc length can be determined by the formula: L = R * C, where L is the arc length (in this case, the distance we intend to cover), R is the radius of the circle (equal to Earth's radius), and C signifies the angle we need to travel. Notably, if two cities are positioned halfway around the globe, flying west equates to a 180° angle. This provides us an arc length of: (calculated values). Heading north requires traveling to 90° latitude and then descending to 17° latitude, therefore the angle becomes: C=2*(90-17)=146°. This results in a different arc length (calculated). Consequently, flying north is indeed shorter by 2349.91 miles.
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