9.6 SPM Practice (Long Questions)

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.

(a) State the location of C.

(b) Calculate the shortest distance, in nautical mile, from A to C measured along the surface of the earth.

(c) Calculate the distance, in nautical mile, from A due east B measured along the common parallel of latitude.

(d) An aeroplane took off from 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.


(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)
$\begin{array}{l}\left(\text{i}\right)\\ \text{Distance travel from }B\text{ to }D\\ =420\times 6\frac{1}{2}\leftarrow \boxed{\begin{array}{l}\text{ Distance travelled}\\ \text{ = average speed }\times \text{ time taken }\end{array}}\\ =2730\text{ nautical miles}\\ \\ \left(\text{ii}\right)\\ \text{Difference in latitude between }B\text{ to }D\\ =\frac{2730}{60}\\ ={45.5}^{\text{o}}\\ \\ \therefore \text{Latitude of }D=\left({53}^{\text{o}}-{45.5}^{\text{o}}\right)N\\ ={7.5}^{\text{o}}N\end{array}$