Theory question 111
Latitude and LongitudeAn aeroplane flies due west for 3 hours from P(lat 50°N, long 60°W) to point Q at an average speed of 600kmh−1. The aeroplane then flies due south from Q to a point Y 500 km away. Calculate, correct to 3 significant figures. (a) the longitude of Q (b) the latitude of Y. [Take the radius of the earth to be 6400 km and π = 22/7]
Show the model answer
Model answer
(a) Distance PQ = 600 × 3 = 1800 km along latitude 50°N.
1800 = θ/360 × 2 × 22/7 × 6400 cos 50°, so θ = 1800 × 360/(2 × 22/7 × 6400 × 0.6428) ≈ 25.1°.
Flying west from 60°W: longitude of Q = 60 + 25.1 = 85.1°W.
(b) 500 = α/360 × 2 × 22/7 × 6400, so α ≈ 4.47°.
Flying south from 50°N: latitude of Y = 50 − 4.47 ≈ 45.5°N.
Explanation
Along a latitude use radius R cos(latitude); along a meridian use the full radius R.