Question

When aero plane left town P (65º N,15º E) to another town Q (65º N,165º W) at a speed of 200 knots using the shortest route. Take π = ²²/₇ and radius of the earth R= 6370 km.

1.  
   • Calculate the distance travelled in nautical miles. 
   • Calculate the time taken to travel from P to Q in hours. 
2. Another plane left P at 1.30 pm local time and travelled to T (65ºN,60ºE) along a parallel of latitude. Calculate the:
   • Distance between P and T to the nearest km 
   • Local time of arrival at town T if the plane flew at the speed of 470 km/h

Answer 1

1.   
   • θ = 180º - (65 + 65) =50º
     D= 60x50 = 3000nm
        
   •   Time = ^d/_s = ^3000nm/_200knots = 15hours
2.     
   •  Distance between P and T to the nearest km (3 marks)
     Longitude difference = 60 - 15 = 45º
     Distance(km) =( ^θ/₃₆₀ )2πRcos α
     ⁴⁵/₃₆₀ x 2 x ²²/₇ x 6370 x cos65
     =2115km
      
   •  Time = ^2115.2/₄₇₀ = 4hrs 30 minutes
     45 x ⁴/₆₀ = 3hrs
     time at T = 1:30  + 4¹/₂ + 3hrs
     =9:00pm