The displacement of a body is the distance that exists between the starting point and the end point of the trajectory of an object.
It is represented by a vector and does not depend on the path made by the object, but on the final and initial point.
To calculate this vector 'd' we do the following procedure.
Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the initial and final points of the trajectory of a body, so, the vector d is:
[tex]d = [x_2-x_1]i + [y_2-y_1]j[/tex]
For the given problem we are told that the object starts the movement from the origin, which is the point (0,0) and ends at the point (0, -8)
Then the vector is:
[tex]d = [0 - 0]i + [-8 - 0]j\ m[/tex]
[tex]d = -8j\ m[/tex]
Then the displacement has a magnitude of 8 meters
