Math

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

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  1. 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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