9.6 SPM Practice (Long Questions)

Question 4:
P (25^o N, 35^o E), Q (25^o N, 40^o W), R and S are four points on the surface of the earth. PS is the diameter of the common parallel of latitude 25^o N.

(a) Find the longitude of S.

(b) R lies 3300 nautical miles due south of P measured along the surface of the earth.
Calculate the latitude of R.

(c) Calculate the shortest distance, in nautical mile, from P to S measured along the surface of the earth.

(d) An aeroplane took off from R and flew due north to P. Then, it flew due west to Q.
The total time taken for the whole flight was 12 hours 24 minutes.

(i) Calculate the distance, in nautical mile, from P due west Q measured along the common parallel of latitude.
(ii) Calculate the average speed, in knot, of the whole flight.

Solution:
(a)
Longitude of S = (180^o – 35^o) W = 145^o W

(b)
$\begin{array}{l}\angle POR=\frac{3300}{60}\\ ={55}^o\\ \text{Latitude of }R={\left(55-25\right)}^o\\ ={30}^{o}S\end{array}$

(c)
Shortest distance from P to S
= (65 + 65) x 60
= 130 x 60
= 7800 nautical miles

(d)(i)
Distance of PQ
= (35 + 40) x 60 x cos 25^o
= 75 x 60 x cos 25^o
= 4078.4 nautical miles

$\begin{array}{l}\left(\text{ii}\right)\\ \text{Total distance travelled}\\ RP+PQ\\ =3300+4078.4\\ =7378.4\text{ nautical miles}\\ \\ \text{Average speed =}\frac{\text{Total distance travelled}}{\text{Time taken}}\\ =\frac{7378.4}{12.4}\leftarrow \boxed{\text{12 hours 24 min}=12+\frac{12}{60}=12+0.4}\\ =595.0\text{ knot}\end{array}$