 # 9.6 Earth as a Sphere, SPM Paper 2 (Long Questions)

Question 3:
P(25o S, 40o E), Qo N, 40o E), R(25o S, 10o W) and are four points on the surface of the earth. PK is the diameter of the earth.
(a) State the location of point K.
(b) Q is 2220 nautical miles from P, measured along the same meridian.
Calculate the value of θ.
(c) Calculate the distance, in nautical mile, from P due west to R, measured along the common parallel of latitude.
(d) An aeroplane took off from Q and flew due south to P. Then, it flew due west to R. The average speed of the aeroplane was 600 knots.
Calculate the total time, in hours, taken for the whole flight.
(a)
As PK is the diameter of the earth, therefore latitude of K = 25o N
Longitude of K= (180o – 40o) W = 140o W
Therefore, location of K = (25o N, 140oW).

(b)
Let the centre of the earth be O.
$\begin{array}{l}\angle POQ=\frac{2220}{60}\\ \text{}={37}^{o}\\ {\theta }^{o}={37}^{o}-{25}^{o}={12}^{o}\\ \therefore \text{The value of}\theta \text{is 12}\text{.}\end{array}$

(c)
Distance from to R
= (40 + 10) × 60 × cos 25o
= 50 × 60 × cos 25o
= 2718.92 n.m.

(d)
Total distance travelled
= distance from to P + distance from P to R
= 2220 + 2718.92
= 4938.92 nautical miles
$\begin{array}{l}\text{Time taken =}\frac{\text{total distance from}Q\text{to}R}{\text{average speed}}\\ \text{}=\frac{4938.92}{600}\\ \text{}=8.23\text{hours}\end{array}$

Question 4:
Diagram below shows the locations of points A (34o S, 40o W) and B (34o S, 80o E) which lie on the surface of the earth. AC is a diameter of the common parallel of latitude 34o 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 34o 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 = (180o – 40o) E = 140o E

(b)
Distance of AB
= (40 + 80) x 60 x cos 34o
= 120 x 60 x cos 34o
= 5969 nautical miles

(c)

(d)