I did this problem and got it correct what I require is the reasoning of the com

Question

I did this problem and got it correct what I require is the reasoning of the components why did we have to choose them. please describe the reasoning and the explanation i know the answer.

1. A plane leaves the airport in Galisteo and flies 170 km at 68 east of north and then changes direction to fly 230 km at 48 south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, A) in which direction and how far should this crew fly to go directly to this plane? B) Write your answer in part A in terms of unit vectors.

Explanation / Answer

Let;s look at the figure provided, and let's calculate the net displacement along x axis and y axis

X ( displacement along x axis) =170 sin 68 + 230 cos 48 = 311.52 km

Y ( displacement along y axis) = 170 cos 68 - 230 sin 48 =-107.24 km ( along - ve Y axis)

Displacement = sqroot ( X^2+Y^2) =329.46 km

displacement in vector form = 311.52 i - 107.24 j

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