Question

A delivery man starts at the post office, drives 40 km north, then 20 km west, then 60 km northeast, and finally 50 km north to stop for lunch. use a graphical method to find his net displacement vector.

Answer 1

assuming north-south along the Y-axis and east-west along the X-axis

X = total X-displacement

from the graph , total displacement along X-direction is given as

X = 0 - 20 + 60 Cos45 + 0

X = 42.42 - 20

X = 22.42 m

Y = total Y- displacement

from the graph , total displacement along Y-direction is given as

Y = 40 + 0  + 60 Sin45 + 50

Y = 90 + 42.42

Y = 132.42 m

magnitude of the net displacement vector using Pythagorean theorem is given as

magnitude : Sqrt(X² + Y²) = Sqrt(22.42² + 132.42²) = 134.31 m

Direction : tan⁻¹(Y/X) = tan⁻¹(132.42/22.42) = 80.4 deg north of east