SPM Mathematics 2016, Paper 2 (Questions 15 & 16)


Question 16 (12 marks):
A(25o N, 35o E), B(25o N, 40o W), C and D are four points which lie on the surface of the earth. AD is the diameter of the common parallel latitude 25o N .
(a) Find the longitude of D.

(b)
C lies 3300 nautical miles due south of measured along the surface of the earth.
Calculate the latitude of C.

(c)
Calculate the shortest distance, in nautical mile, from to measured along the surface of the earth.

(d)
An aeroplane took off from C and flew due north to point A. 
The total time taken for the whole flight was 12 hours 24 minutes.

(i)
Calculate the distance, in nautical mile, from A due west to measured along the common parallel of latitude.

(ii)
Calculate the average speed, in knot, of the whole flight.


Solution:
(a) 
Longitude of D = (180o – 35o)W
= 145oW

(b)
AOC= 3300 60 = 55 o Latitude of C = ( 5525 ) o S = 30 o S

(c) 
Shortest distance of to D
= (65o + 65o) × 60’
= 130o × 60’
= 7800 nautical miles

(d)(i) 
Distance from A to B
= (35o + 40o) × 60’ × cos 25o
= 75o × 60’ × cos 25o
= 4078.4 nautical miles

(d)(ii)
Total distance travelled =CA+AB =3300+4078.4 =7378.4 nautical miles Average speed= Total distance Total time = 7378.4 12.4  knot =595.0 knot


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