9.6 SPM Practice (Long Questions)


Question 1:
Diagram below shows four points P, Q, R and M, on the surface of the earth. 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 = latitude of Q = 40o N
Longitude of = (70o – 25o) W = 45o W
Longitude of = (180o – 45o) E = 135o E
Therefore, position of R = (40o N, 135oE).
 
(b)
Shortest distance from Q to R
= (180 – 40 – 40) x 60
= 100 × 60
= 6000 nautical miles
 
(c)
P O M = 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 = ( 180 25 ) × 60 × cos 40 o 660 = 155 × 60 × cos 40 o 660 = 10.79 hours