ohn and Jack are planning to do a physics lab related to vectors. Starting at the door of their physics classroom, they walk 2.0 meters, south. They make a right hand turn and walk 16.0 meters, west. They turn right again and walk 24.0 meters, north. They then turn left and walk 36.0 meters, west. What is the magnitude of their overall displacement?

Answer 1

D=2m[270o] + 16m[180o] + 24m[90o]+36m[180o].
Add the two 180o vectors directly:
D = 2[270o] + 52[180o] + 24[90o]

X = 2*cos270+52*cos180+24*cos90 = -52 m.
Y = 2*sin270+52*sin180+24*sin90 = 22 m.

D^2 = (-52)^2 + 22^2 = 3188
D = 56.5 m.