An airplane starting from airport A ?ies 848 km east, then 472 km at 74.2? west

Question

An airplane starting from airport A ?ies 848 km east, then 472 km at 74.2? west of north, and then 885 km north to arrive ?nally at airport B. The next day, another plane ?ies directly from A to B in a straight line.

a.) In what direction should the pilot travel in this direct ?ight? Use counterclockwise
as the positive angular direction from due east, between the limits of -180? and 180?.
Assume there is no wind during these ?ights. Answer in units of ?

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

Explanation / Answer

change the directions into x y component, positive x is east and positive y is north
first part: (848i + 0j)
second part: (-472cos74.2 i + 472sin74.2 j) = (-128.52i + 454.17j)
thirt part: (0i + 885j)

total = (848i + 0j) + (-128.52i + 454.17j) + (0i + 885j) = (719.48i + 1339.17j)

a) direction = tan-1(1339.17/719.48) = 61.753 degree north due east.

b) magnitude = (719.482 + 1339.172) = 1520.19 km

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