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Question

A car travels 6km towards north at an angle of 45o to the east and then travels distance of 4km towards north at an angle of 135o to the east (Figure). How far is the point from the starting point? What angle does the straight: line joining its initial and final position makes with the east?
984317_db11bce0a56c49759fd0ac23154b9d64.png

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Solution

Net movement along x-direction,
Sx=(64)cos45o^i=2×12=2km
Net movement along y-direction,
Sy=(6+4)sin45o^j=10×12=52km
Net movement from startinf point,
s|=S2x+S2y=(2)2+(52)2=52km
Angle which makes with the east direction,
tanθ=Y-componentX-component=522
θ=tan1(5)

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