An ambitious hiker walks 25 km west and then 35 km south in a day. find the magnitude and direction of the hikers resultant displacement (relative to due west).

Refer to the diagram shown below.

The resultant displacement, d, is the vector sum of distances traveled west and south.

The magnitude of d is
d = √(25² + 35²) = 43.012 km

The angle that d makes below due west (or south of west) s
θ = tan⁻¹ (35/25) = 54.5°

The resultant displacement is 43.0 km, at an angle of 54.5° south relative to due west.

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.