Let's first find x- and y-components of the resultant displacement:
dx=6 mi⋅cos0∘+15 mi⋅cos90∘+1 mi⋅cos180∘+3 mi⋅cos270∘=5 mi,
dy=6 mi⋅sin0∘+15 mi⋅sin90∘+1 mi⋅sin180∘+3 mi⋅sin270∘=12 mi.
We can find the magnitude of the resultant displacement from the Pythagorean theorem:
d=dx2+dy2=(5 mi)2+(12 mi)2=13 mi.We can find the direction of the resultant displacement from the geometry:
θ=tan−1(dxdy),θ=tan−1(5 mi12 mi)=67.4∘ N of E.
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