Theory question 108
Latitude and LongitudeA plane flies due East from A (lat. 53°N, long. 25°E) to a point B (lat. 53°N, long. 85°E) at an average speed of 400 km/h. The plane then flies South from B to a point C 2000 km away. Calculate, correct to the nearest whole number: (a) the distance between A and B; (b) the time the plane takes to reach point B; (c) the latitude of C. [Take the radius of the earth to be 6400 km and π = 22/7].
Show the model answer
Model answer
(a) Difference in longitude = 85 − 25 = 60°. AB = 60/360 × 2 × 22/7 × 6400 × cos 53° = 6704.8 × 0.6018 ≈ 4035 km.
(b) Time = 4035 ÷ 400 ≈ 10.09 h ≈ 10 hours.
(c) 2000 = θ/360 × 2 × 22/7 × 6400, so θ ≈ 17.9°. Latitude of C = 53 − 17.9 = 35.1 ≈ 35°N.
Explanation
Along a latitude use R cos(latitude); along a meridian use R.