**Question 6:**

Diagram below shows the locations of points

*P*,

*Q*,

*R*,

*A*,

*K*and

*C*, on the surface of the earth.

*O*is the centre of the earth.

(a) Find the location of

*A*.

(b) Given the distance

*QR*is 3240 nautical miles, find the longitude of

*Q*.

(c) Calculate the distance, in nautical miles of

*KA*, measured along the common parallel latitude.

(d) An aeroplane took off from

*A*and flew due west to

*K*along the common parallel of latitude. Then, it flew due south to

*Q*. The average speed of the aeroplane was 550 knots.

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

*Solution:***(a)**

Longitude of

*A*= (180

^{o}– 15

^{o}) = 165

^{o}E

Latitude of

*A*= 50

^{o}N

**position of**

*A*= (50^{o}N, 165^{o}E).**(b)**

$\begin{array}{l}\angle QOR=\frac{3240}{60}\\ \text{}={54}^{o}\\ \therefore \text{Longitudeof}Q=({165}^{o}-{54}^{o})E\\ \text{}={111}^{o}E\end{array}$

**(c)**

Distance of

*KA*

= 54 x 60 x cos 50

^{o}= 2082.6 nautical miles

**(d)**

$\begin{array}{l}\text{Totaldistance}=AK+KQ\\ \text{}=2082.6+\left(50\times 60\right)\\ \text{}=5082.6\text{nauticalmiles}\\ \\ \text{Totaltime}=\frac{5082.6}{550}\\ \text{}=9.241\text{hours}\end{array}$