**Question 3:**

Diagram below shows the locations of points

*A*(34

^{o}S, 40

^{o}W) and

*B*(34

^{o}S, 80

^{o}E) which lie on the surface of the earth.

*AC*is a diameter of the common parallel of latitude 34

^{o}S.

(a) State the longitude of

*C.*

(b) Calculate the distance, in nautical mile, from

*A*due east to

*B*, measured along the common parallel of latitude 34

^{o}S.

(c)

*K*lies due north of

*A*and the shortest distance from

*A*to

*K*measured along the surface of the earth is 4440 nautical miles.

Calculate the latitude of

*K*.

(d) An aeroplane took off from

*B*and flew due west to

*A*along the common parallel of latitude. Then, it flew due north to

*K*. The average speed for the whole flight was 450 knots.

Calculate the total time, in hours, taken for the whole flight.

*Solution:*

**(a)**

Longitude of

*C*= (180

^{o}– 40

^{o}) E = 140

^{o}E

**(b)**

Distance of

*AB*

= (40 + 80) x 60 x cos 34

^{o}= 120 x 60 x cos 34

^{o}= 5969 nautical miles

**(c)**

$\begin{array}{l}\angle AOK=\frac{4440}{60}\\ \text{}={74}^{o}\\ \text{Latitudeof}K={\left(74-34\right)}^{o}N\\ \text{}={40}^{o}N\end{array}$

**(d)**

$\begin{array}{l}\text{Totaldistancetravelled}\\ BA+AK\\ =5969+4440\\ =10409\text{nauticalmiles}\\ \\ \text{Totaltimetaken=}\frac{\text{Totaldistancetravelled}}{\text{Averagespeed}}\\ \text{}=\frac{10409}{450}\\ \text{}=23.13\text{hours}\end{array}$