**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)

(b)

*C*lies 3300 nautical miles due south of

*A*measured along the surface of the earth.

Calculate the latitude of

*C*.

**Calculate the shortest distance, in nautical mile, from**

(c)

(c)

*A*to

*D*measured along the surface of the earth.

**An aeroplane took off from**

(d)

(d)

*C*and flew due north to point

*A.*

The total time taken for the whole flight was 12 hours 24 minutes.

**Calculate the distance, in nautical mile, from**

(i)

(i)

*A*due west to

*B*measured along the common parallel of latitude.

**Calculate the average speed, in knot, of the whole flight.**

(ii)

(ii)

*Solution*:**(a)**

Longitude of

*D*= (180

^{o}– 35

^{o})W

= 145

^{o}W

**(b)**

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

**(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)**

$\begin{array}{l}\text{Totaldistancetravelled}\\ =CA+AB\\ =3300+4078.4\\ =7378.4\text{nauticalmiles}\\ \\ \text{Averagespeed}=\frac{\text{Totaldistance}}{\text{Totaltime}}\\ =\frac{7378.4}{12.4}\text{knot}\\ =595.0\text{knot}\end{array}$