Suppose you first walk 21.0 m in a direction 30.0° west of north and then 38.0 m

Question

Suppose you first walk 21.0 m in a direction 30.0° west of north and then 38.0 m in a direction 45.0° south of west. Find the magnitude of the displacement. (If you represent the two legs of the walk as vector displacements [(A)ec] and [(B)ec], as in Figure below, then this problem asks you to find their vector sum [(R)ec] = [(A)ec] + [(B)ec].)

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What is the compass direction of a line connecting your starting point to your final position? 12.8deg S of W Submit Answer Incorrect.

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Explanation / Answer

so given
initial displacement, A = 21(-sin(30)i + cos(30)j) [ assuming that i is a unit vector along east and j is a unit vector along north]
second displacement = B = -38(sin(45)i + cos(45)j)

so net displacement = A + B = 21(-sin(30)i + cos(30)j) -38(sin(45)i + cos(45)j) = -37.37i -8.683 j

so magnitude of resultant = sqroot(37.37^2 + 8.683^2) = 38.365 m

hence the person walks 38.365 m

direction = arctan(8.683/37.37) = 13.08 deg south of west

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