Problem 81.

An object travels a distance of 5 km towards east, then 4 km towards north and finally 10 km towards east

1) what is total traveled distance?

2) what is resultant displacement?

Solution:

We show each displacement (travelled paths) in the figure.

(1) The total traveled distance is the sum of all traveled distances. It does not matter what the relative directions of displacements are, we just need to add the magnitude of displacements:

(2) The second part of the problem is easier to solve in terms of components of vectors.

The net (resultant) displacement is the vector sum of three displacements: the first displacement ( ), the second displacement ( ), and the third displacement ( ):

Then we can find the x and y components of the displacement vectors and finally the net displacement:

Then the magnitude of the net displacement is