**Question 1**

Diagram below shows four points

*P*,*Q*,*R*and*M*, on the surface of the earth.*P*lies on longitude of 70^{o}W.*QR*is the diameter of the parallel of latitude of 40^{o }N.*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}NLongitude of

*Q*= (70^{o}– 25^{o}) W = 45^{o}WLongitude of

*R*= (180^{o}– 45^{o}) E = 135^{o}ETherefore,

**position of***R*= (40^{o}N, 135^{o}E).

**(b)**

Shortest distance from

*Q*to*R*= (180 – 40 – 40) x 60

= 100 × 60

=

**6000 nautical miles**

**(c)**

**(d)**