2. Two towns P and Q are already opposite each other on the longitude. P(30°N, 40°E) and Q(30°N, 140°W) are on the surface of the earth.
i) Find the distance along P and Q along the great circle in km, ii) Calculate the distance along the small circle between P and Q giving your answer in a) nm, b) km iii) Which distance is shorter in km and by how much?
| The angle difference along the great circle=180-(+= |
| Distance PQ along the great circle=°/360*2*22/7*6370 |
| PQ=km(to the nearest whole number) |
| i. The longitude angle difference=140°+40°= |
| Since they are on the opposite side of the meridian. |
| ii. Distance along the small circle in nm= *60 cos=*60 cos = |
| (to the nearest whole number) |
| iii. Distance along the small circle in km= /360 * 2πR cos |
| /360*2*22/7*6370*cos ° |
| km (to the nearest whole number) |