Theory question 112
Latitude and LongitudeAn aeroplane flies from a town P (lat. 40°N, 38°E) to another town Q (lat. 40°N, 22°W). It later flies to a third town T (28°N, 22°W). Calculate the: (a) distance between P and Q along their parallel of latitude; (b) distance between Q and T along the line of longitudes. (c) average speed at which the aeroplane will fly from P to T via Q, if the journey takes 12 hours, correct to three significant figures. (Take the radius of the earth to be 6400km and π = 3.142)
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(a) Difference in longitude = 38° + 22° = 60°
PQ = 60/360 × 2 × 3.142 × 6400 × cos 40° = 5135km ≈ 5130km
(b) Difference in latitude = 40° − 28° = 12°
QT = 12/360 × 2 × 3.142 × 6400 = 1341km ≈ 1340km
(c) Total distance ≈ 6475km; speed = 6475 ÷ 12 ≈ 540km/h
Along a parallel of latitude use the radius R cos(latitude); along a meridian use R.