An athletics coach traces the path of a runner along a straight practice track. The starting line is chosen as the origin O. The runner begins 50m east of O, runs 120m west to point A, immediately turns and runs 180m east to point B, and finally runs 30m west to finish at point C.
(a) Calculate the position of the runner relative to O after reaching each point A, B, and C.
(b) Find the total distance covered from the start to point C.
(c) Determine the net displacement of the runner from O to point C, stating both magnitude and direction.
(d) Show, using your answers to parts (b) and (c), that the magnitude of displacement is less than or equal to the distance travelled for this journey.