A person walks 500m due north, turns and walks 300m due west, and finally walks 800m due south. Determine the persons resultant displacement from her starting point.

Suppose a moving object starts from point A and travels through a determined path to point B. The distance is the sum of all the partial distances traveled, and the displacement is the vector directed from A to B.

The path of the person is shown in the image below. Note the 500 m due north and the 800 m due south produce a distance of 300 m due south. The displacement vector D is the resultant of the whole movement.

To find the magnitude of the displacement, we need to calculate the hypotenuse of a triangle of sides 300 m (already described) and 300 m, marked in red.

The magnitude of D is:

[tex]\mid D \mid = \sqrt{300^2+300^2}[/tex]

[tex]\mid D \mid = \sqrt{90000+90000}[/tex]

[tex]\mid D \mid = \sqrt{180000}[/tex]

[tex]\mid D \mid = 424.26\ m[/tex]

A person walks 500m due north, turns and walks 300m due west, and ￼finally walks 800m due south. Determine the persons resultant displacement from her starting point.

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A person walks 500m due north, turns and walks 300m due west, and finally walks 800m due south. Determine the persons resultant displacement from her starting point.