An 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 their 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 3 significant figures. [Take the radius of the earth = 6400km ; (pi = 3.142)]
Explanation
(a) Distance along arc PQ = (frac{theta}{360°} times 2 pi r)
where (r = R cos theta)
(|PQ| = frac{60°}{360°} times 2 times frac{22}{7} times 6400 times cos 40°)
(|PQ| = frac{1}{6} times 2 times frac{22}{7} times 6400 times 0.7660)
= (5134.74 km approxeq 5135km) (to the nearest whole number)
(b) Difference in latitude between Q and T = 40° – 28° = 12°
(therefore |QT| text{along the line of longitude} = frac{12}{360} times 2 times frac{22}{7} times 6400)
(frac{1}{30} times 2 times frac{22}{7} times 6400 = 1340.95km approxeq 1341km)
(c) Average speed = (frac{text{Total distance covered}}{text{Total time taken}})
= (frac{5134.74 + 1340.95}{12} = 539.64km/hr)
(approxeq 540km/hr) (to 3 significant figures)