Earth as a Sphere, Long Questions (Question 1)


Question 1
Diagram below shows four points P, Q, R and M, on the surface of the earth. P lies on longitude of 70oW. QR is the diameter of the parallel of latitude of 40o N. M lies 5700 nautical miles due south of P.
(a) Find the position of R.
(b) Calculate the shortest distance, in nautical miles, from Q to R, measured along the surface of the earth.
(c) Find the latitude of M.
(d) An aeroplane took off from R and flew due west to P along the parallel of latitude with an average speed of 660 knots.
Calculate the time, in hours, taken for the flight.

Solution:
(a)
Latitude of R = latitude of Q = 40o N
Longitude of Q = (70o – 25o) W = 45o W
Longitude of R = (180o – 45o) E = 135o E
Therefore, position of R = (40o N, 135o E).

(b)
Shortest distance from Q to R
= (180 – 40 – 40) x 60
= 100 x 60
= 6000 nautical miles

(c)
POM= 5700 60             = 95 o Latitude of M=( 95 o 40 o )S                          = 55 o S

(d)
Time taken = distance from R to P average speed                     = ( 18025 )×60×cos 40 o 660                     = 155×60×cos 40 o 660                     =10.79 hours