9.6 SPM Practice (Long Questions)

Question 8 (12 marks):
Diagram 8 shows four points, G, H, I and J on the surface of the Earth. JI is the diameter of the parallel of latitude 50^o N. O is the centre of the Earth.

Diagram 8

(a) State the location of G.

(b) Calculate the shortest distance, in nautical mile, from I to J measured along the surface of the Earth.

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

(d) An aeroplane took off from I and flew due south to point P. The average speed of the journey was 800 knots. The time taken for the flight was 5.25 hours.
Calculate the latitude of P.


Solution:
(a)
Location of G = (70^o S, 20^o W)

(b)
∠ JOI
= 180^o – 50^o – 50^o 
= 80^o
Distance of I to J
= 80^o × 60’
= 4800 nautical miles

(c)
Distance of G to H
= (20^o + 120^o) × 60’ × cos 70^o
= 140^o × 60’ × cos 70^o
= 2872.97 nautical miles

(d)
$\begin{array}{l}\text{Average speed}=\frac{\text{Total distance travelled}}{\text{Total time taken}}\\ 800=\frac{x}{5.25}\\ x=4200\text{ nautical miles}\\ I\text{ to }P=4200\\ \\ \text{Difference between parallel}=y\\ y\times 60=4200\\ y={70}^o\\ \\ \text{Thus, latitude of }P\\ ={70}^o-{50}^o\\ ={20}^{o}S\end{array}$