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• Q7: a) A plane station P (30°N, 50°E) flies toward a station Q at a latitude of 30°N. If it flies along a constant latitude, find where it strikes the longitude of 80°E.

  b) The location of two airports is S (35°N, 10°E) and T (35°N, 45°E). Find the distance between them in kilometers.

Let's break it down:

a) Finding the longitude when the plane reaches 80°E:

The plane flies along a constant latitude of 30°N. To calculate the distance or point where it strikes the longitude of 80°E, you'd use the formula for great-circle distances for specific longitudes.

Since this part is mostly about understanding when it reaches a longitude of 80°E at the same latitude of 30°N, I'll give a brief explanation afterward for clarity.

b) Finding the distance between two points at the same latitude (35°N):

To find the distance between two points S (35°N, 10°E) and T (35°N, 45°E), both of which lie on the same latitude, we can use the following formula for the distance between two points on the same parallel of latitude: $D = \Delta \lambda \times \cos(\phi) \times \frac{\pi R}{180}$ Where:

• $\Delta \lambda$ is the difference in longitudes.
• $\phi$ is the latitude (35°N in this case).
• $R$ is the Earth's radius (approximately 6371 km).
• The cosine accounts for the curvature of the Earth as you move along a specific latitude.

Let me calculate that for you now.The distance between the two airports S (35°N, 10°E) and T (35°N, 45°E) along the same latitude is approximately 3188 km.

Would you like further clarification on any part of this or details on how the calculations were done? Here are five related questions to consider:

1. How do you calculate great-circle distances for points not on the same latitude?
2. What is the difference between great-circle distance and Euclidean distance?
3. How does Earth's curvature affect distance calculations?
4. What is the significance of latitude and longitude in distance calculations?
5. How would the result change if we used a different radius for Earth, such as the polar radius?

Tip: The cosine factor in the formula accounts for the Earth's curvature, reducing the distance as you move away from the equator.