**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

(a)

*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)

(b)

*∠ JOI*

= 180

^{o}– 50

^{o}– 50

^{o}

= 80

^{o}Distance of

*I*to

*J*

= 80

^{o}× 60’

= 4800 nautical miles

**Distance of**

(c)

(c)

*G*to

*H*

= (20

^{o}+ 120

^{o}) × 60’ × cos 70

^{o}= 140

^{o}× 60’ × cos 70

^{o}= 2872.97 nautical miles

(d)

(d)

$\begin{array}{l}\text{Averagespeed}=\frac{\text{Totaldistancetravelled}}{\text{Totaltimetaken}}\\ 800=\frac{x}{5.25}\\ x=4200\text{nauticalmiles}\\ I\text{to}P=4200\\ \\ \text{Differencebetweenparallel}=y\\ y\times 60=4200\\ y={70}^{o}\\ \\ \text{Thus,latitudeof}P\\ ={70}^{o}-{50}^{o}\\ ={20}^{o}S\end{array}$