Theory question 112
Latitude and LongitudeAn aeroplane flies due north from a town T on the equator at a speed of 950 km per hour for 4 hours to another town P. It then flies eastwards to town Q on longitude 65° E. If the longitude of T is 15° E, (a) represent this information in a diagram. (b) calculate the: (i) latitude of P, correct to the nearest degree; (ii) distance between P and Q, correct to 4 significant figures. [Take π = 22/7, Radius of the earth = 6400 km]
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(a) Sketch of the earth with the equator, the meridian 15°E through T and P, and the parallel through P to Q on 65°E.
(b)(i) T to P = 950 × 4 = 3800 km. θ/360 × 2 × 22/7 × 6400 = 3800 → θ ≈ 34.0°, so P is about 34°N.
(ii) Longitude difference = 50°. PQ = 50/360 × 2 × 22/7 × 6400 × cos 34° ≈ 5587.3 × 0.8290 ≈ 4632 km.
Along a parallel of latitude the radius is R cos(latitude).