9.6 SPM Practice (Long Questions)

Question 9 (12 marks):
A(25^o N, 35^o E), B(25^o N, 40^o W), C and D are four points which lie on the surface of the earth. AD is the diameter of the common parallel latitude 25^o N .
(a) Find the longitude of D.

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

(c) Calculate the shortest distance, in nautical mile, from A to D 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 B measured along the common parallel of latitude.

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


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

(b)
$\begin{array}{l}\angle AOC=\frac{3300}{60}={55}^o\\ \text{Latitude of }C\\ ={\left(55-25\right)}^{o}S\\ ={30}^{o}S\end{array}$

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

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

(d)(ii)
$\begin{array}{l}\text{Total distance travelled}\\ =CA+AB\\ =3300+4078.4\\ =7378.4\text{ nautical miles}\\ \\ \text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}\\ =\frac{7378.4}{12.4}\text{ knot}\\ =595.0\text{ knot}\end{array}$