London is situated at longitude 0o, latitude 52o North and
Cape Town at longitude 18o East, latitude 34o South. Taking
the earth to be a sphere with unit radius (and ultimately scaling
by 6367 kilometres for the radius of the earth) work out
coordinates for both places, then find the angle LOC where L
represents London, O the centre of the earth and C Cape Town.
Hence find the distance on the surface of the earth between the
two places. If a plane flies at an altitude of 6 kilometres and
the journey takes 11 hours what is the average speed?
[You might also like to try the problems
'Over The Pole', which isa little simpler, and
'Flight Path' which is similar to 'Air Routes' but the method
of solution given there is a bit different. ]