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Classical Mechanics Vector Analysis (Airplane in Wind)

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Vector analysis problem taken from Classical Mechanics, 5th Edition, by Tom W.B. Kibble and Frank Berkshire. The problem states:
An aircraft is to fly to a destination 800 km due north of its starting point. Its airspeed is 800 km/h. The wind is from the east at a speed of 30 m/s. On what compass heading should the pilot fly? How long will the flight take? If the wind speed increases to 50 m/s, and the wind backs to the north-east, but no allowance is made for this change, how far from its destination will the aircraft be at its expected arrival time?
Kibble, T. W. B., and F. H. Berkshire. Classical Mechanics. 5th ed. London: Imperial College, 2004. Print.
An aircraft is to fly to a destination 800 km due north of its starting point. Its airspeed is 800 km/h. The wind is from the east at a speed of 30 m/s. On what compass heading should the pilot fly? How long will the flight take? If the wind speed increases to 50 m/s, and the wind backs to the north-east, but no allowance is made for this change, how far from its destination will the aircraft be at its expected arrival time?
Kibble, T. W. B., and F. H. Berkshire. Classical Mechanics. 5th ed. London: Imperial College, 2004. Print.
Classical Mechanics Vector Analysis (Airplane in Wind)
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