(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 fro...
Question 1 Report
(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; \(\pi = \frac{22}{7}\)].
Answer Details
(a) Distance A to B along the parallel of latitude 53°N, through a longitude difference of \(85^\circ - 25^\circ = 60^\circ\):
\[AB = \frac{60}{360}\times 2\pi R\cos53^\circ = \frac{60}{360}\times 2\times\frac{22}{7}\times6400\times\cos53^\circ.\]
\[AB = \frac{1}{6}\times 40228.6\times0.6018 = 4035\text{ km (to the nearest km)}.\]
(b) Time to reach B at 400 km/h:
\[t = \frac{4035}{400} = 10.09 \approx 10\text{ hours}.\]
(c) Latitude of C. Flying south along a meridian, 1° corresponds to
\[\frac{2\pi R}{360} = \frac{1}{360}\times2\times\frac{22}{7}\times6400 = 111.75\text{ km}.\]
The 2000 km southward change in latitude is
\[\frac{2000}{111.75} = 17.9^\circ.\]
\[\text{Latitude of C} = 53^\circ - 17.9^\circ = 35.1^\circ \approx 35^\circ\text{N}.\]
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