9.6 SPM Practice (Long Questions)

Posted on April 24, 2020 by user

Question 1:

Diagram below shows four points P, Q, R and M, on the surface of the earth. P lies on longitude of 70^oW. QR is the diameter of the parallel of latitude of 40^oN. M lies 5700 nautical miles due south of P.

(a) Find the position of R.

(b) Calculate the shortest distance, in nautical miles, from Q to R, measured along the surface of the earth.

(c) Find the latitude of M.

(d) An aeroplane took off from R and flew due west to P along the parallel of latitude with an average speed of 660 knots.
Calculate the time, in hours, taken for the flight.

Solution:

(a)

Latitude of R = latitude of Q = 40^o N

Longitude of Q = (70^o – 25^o) W = 45^o W

Longitude of R = (180^o – 45^o) E = 135^o E

Therefore, position of R = (40^o N, 135^oE).

(b)

Shortest distance from Q to R

= (180 – 40 – 40) x 60

= 100 × 60

= 6000 nautical miles

(c)

\begin{array}{l} ∠ P O M = \frac{5700}{60} \\ = 95^{o} \\ ∴ Latitude of M = (95^{o} - 40^{o}) S \\ = 55^{o} S \end{array}

(d)

\begin{array}{l} Time taken = \frac{distance from R to P}{average speed} \\ = \frac{(180 - 25) \times 60 \times \cos 40^{o}}{660} \\ = \frac{155 \times 60 \times \cos 40^{o}}{660} \\ = 10.79 hours \end{array}