Question

A man walks $40m$ north, then $30m$ east and then $40m$south. Find the displacement from the starting point.

Answer 1

Hint: First of all express the parameters mentioned in the question in the form of a diagram. Then find the displacement from the initial point. Displacement can be the minimum distance between the final position and initial position of the man. This information will help you in solving this question.

Complete answer:
 First of all let us express the problem diagrammatically. The figure will be like this,

As the man is walking towards the $40m$ north first and then towards the east by a distance of $30m$. Then he is in the motion towards the south direction by a distance same as that of the travel in the north direction. Now he will be exactly perpendicular to the initial position of him. This will be in the form of a rectangle with opposite sides parallel and equal and angles to be perpendicular to each other. Hence the displacement will be equal to the distance travelled by the man in the eastern direction.
That is,
$s=30m$
But the direction will be different. The direction of motion will be towards the western direction which is opposite to that of eastern direction.

Note:
A displacement is defined as a vector quantity where the path length is the shortest distance or the perpendicular distance from the initial to the final position of a point P undergoing motion. Displacement as already mentioned is a vector quantity, is of great importance for the direction also. They depend on both magnitude as well as direction. Distance is the total length of the path of the motion. This is a scalar quantity and has no connection with the direction of motion of the particle.