An airplane starting from airport A flies 444 km east, then 694 km at 55.3 west

Question

An airplane starting from airport A flies 444 km east, then 694 km at 55.3 west of north, and then 850 km north to arrive finally at airport B.

(a) The next day, another plane flies directly from A to B in a straight line. In what direction should the pilot travel in this direct flight? Use counterclockwise as the positive angular direction from due east, between the limits of 180 and 180 Assume there is no wind during these flights. Answer in units of

(b) How far will the pilot travel in this direct flight? Answer in units of km.

Explanation / Answer

rAB= rB - rA = 444i + 694(-sin55.3i + cos55.3j) + 850j

rAB. = -126.6i + 1245j km

This is the displacement vector from A to B.

(A) angle = 180 - tan^-1(1245/126.6) = 95.8 deg

(B) magnitude = sqrt[ (-126.6)^2 + 1245^2)

= 1251.5 km

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