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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

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  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 

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