A hiker starts at a campground designated as position x=0 on a straight east–west trail. The hiker travels in three legs: 1.2 km east, 0.75 km west, and 0.40 km east.
(a) Describe the difference between the hiker’s total distance and the hiker’s displacement for the entire trip. In your description, include how sign conventions along a one–dimensional axis affect the meaning of each quantity.
(b) Taking east to be the positive direction, determine the hiker’s displacement after the three legs. State both the signed value and its magnitude with an appropriate direction.
(c) The magnitude of the displacement is smaller than the total distance the hiker walked. Explain quantitatively and qualitatively why this difference arises in the context of vector addition along a straight line.