An aeroplane flies from town A(20°N,60°E) to townB (20°N,20°E)

if the journey takes 6 hours
Calculate correct to 3 significant figures, the average speed of the aeroplane
If it then flies due north from town B to town C 420km away.calculate to the nearest degree the latitude of town C

4 answers

Approximate the earth as a perfect sphere, with radius 6371 km.

Change in longitude = 60-20 = 40° = 40π/180 radians
Latitude of flight path = 20° N
horizontal radius = Rcos(20°)

Horizontal arc length from A to B
=Rcos(20°)(40π/180)
=6371*0.9397*.6981
=1506.6 km

1506.6 km took 6 hours, so
average ground speed
=1506.6/6
=251.1 km/hr

travelling due north another 420 km subtends an angle
=420/6371 radians
=0.06593 radians
=0.06593*180/π °
=3.78°

Latitude of town C
=20+3.78
=23.78°N

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