Figure a 54 The vanous ines represent paths taken by diflerent people walking in

Question

Figure a 54 The vanous ines represent paths taken by diflerent people walking in a cihy 7. (a) R MM blacks are 120 m on a 5. Suppose you first walk 12.0 m in a direction 20° west of north and then 20.0 m in a direction 40.0 south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B, as in Figure 3.56, then this problem finds their sum R = A + B .)

Explanation / Answer

vector R = vector A + vector B

vector R = -12sin(20 degrees) i + 12cos(20degrees) j - 20cos(40 degrees) i - 20 sin(40 degrees) j

=> vector R = -4.104 i + 11.26 j - 15.32 i - 12.4 j = -19.424 i - 1.14 j

tan(theta) = 1.14/19.424 = 0.0586

=> compass directon theta = 3.35 degrees

distance from starting point = [(19.424)^2 + (1.14)^2]^0.5 = 19.45 m

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