**Question 5:**

*A*(53

^{o}N, 84

^{o}E),

*B*(53

^{o}N, 25

^{o}W),

*C*and

*D*are four points on the surface of the earth.

*AC*is the diameter of the parallel of latitude 53

^{o}N.

**State the location of**

(a)

(a)

*C.*

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

(b)

(b)

*A*to

*C*measured along the surface of the earth.

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

(c)

(c)

*A*due east

*B*measured along the common parallel of latitude.

**An aeroplane took off from**

(d)

(d)

*B*and flew due south to

*D.*The average speed of the flight was 420 knots and the time taken was 6½ hours.

Calculate

**(i)**the distance, in nautical mile, from

*B*to

*D*measured along the meridian.

**(ii)**the latitude of

*D*.

*Solution:***(a)**

Latitude of

*C*= 53

^{o}N

Longitude of

*C*= (180

^{o}– 84

^{o}) E = 96

^{o}E

Therefore location of

*C*= (53

^{o}N, 96

^{o}E)

**(b)**

Shortest distance from

*A*to

*C*

= (180 – 53 – 53) x 60

= 74 x 60

= 4440 nautical miles

**(c)**

Distance from

*A*to

*B*

= (84 – 25) x 60 x cos 53

^{o}= 59 x 60 x cos 53

^{o}= 2130.43 nautical miles

**(d)**

$\begin{array}{l}\left(\text{i}\right)\\ \text{Distancetravelfrom}B\text{to}D\\ =420\times 6\frac{1}{2}\leftarrow \overline{)\begin{array}{l}\text{Distancetravelled}\\ \text{=averagespeed}\times \text{timetaken}\end{array}}\\ =2730\text{nauticalmiles}\\ \\ \left(\text{ii}\right)\\ \text{Differenceinlatitudebetween}B\text{to}D\\ =\frac{2730}{60}\\ ={45.5}^{\text{o}}\\ \\ \therefore \text{Latitudeof}D=\left({53}^{\text{o}}-{45.5}^{\text{o}}\right)N\\ \text{}={7.5}^{\text{o}}N\end{array}$