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1. A boy walk 140 m due north, 85 m due east, 35 m due southeast, 38 m due west and then 19 m due northwest. Calculate the displacement for his whole journey.​

Sagot :

Answer:

141 m at 65.6° N of E

Explanation:

Let E be along the positive x axis of a unit circle

N = 90°

E = 0°

SE = -45°

W = 180°

NW = 135°

east displacement

x = 140cos90 + 85cos0 + 35cos-45 + 38cos180 + 19cos135 = 58.313708... m

north displacement

y = 140sin90 + 85sin0 + 35sin-45 + 38sin180 + 19sin135 = 128.6862915... m

d = √(128.6862915² + 58.313708²) = 141.28216525... m

tanθ = 128.6862915 / 58.313708

θ = 65.622521...

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