How would I solve this practice question?

Question

A person travels 18Km [E], 3 km [E45°N] then 18Km [S]. show that the person's displacement is unaffected by the choice of positive direction?

Answer 1

First, let's make sure you understand displacement. Displacement simply is how far you are from the start. So, if you walk in a circle and end at the beginning spot your displacement is zero.

Next, positive direction means the acceleration (how fast) is in the same direction as the velocity (direction and how fast).

Since we know the total amount of displacement because we know the total amount of travel and direction then it does not matter how fast (positive or negative direction) they get there.

For example: a plane can travel at 500mph around the earth back to the same spot and the displacement is zero. This is true even if the plane travels at 100mph.