(a) A 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 2000km 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 radius of the earth = 6400km; (pi = frac{22}{7})].
Explanation
(a)
Longitude difference = 85° – 25° = 60°.
Distance AB along the parallel of latitude = (frac{theta}{360°} times 2pi R cos alpha)
(AB = frac{60}{360} times 2 times frac{22}{7} times 6400 cos 53)
= (frac{1}{6} times frac{44}{7} times 3851.62)
= (4,035.03 km)
(approxeq 4035 km)
(b) (Speed = frac{Distance}{Time})
(therefore Time = frac{Distance}{Speed})
= (frac{4035}{400})
(approxeq 10 hours).
(c) Distance BC measured along the meridian
(BC = frac{theta}{360} times 2 pi R)
(2000 = frac{theta}{360} times 2 times frac{22}{7} times 6400)
(theta = 17.898° approxeq 18°)
(theta) = Latitude difference
Let the latitude of C = x.
(theta = 53 – x)
(18 = 53 – x)
(x = 35°)