A man walks 2.0 km directly south-west, then 4.0 km east and finally 6.0 km north east. Specify the x and y coordinates of his final position with reference to his starting point(in km). What is his displacement w.r.t. to his starting point?

The figure below depicts the path travelle dby the man

OA = 2km

AB = OC' = 4km

BC' = 2km

BC = 6km

and

CC' = 6 - 2km = 4km

here we have to find the coordinates of C

so,

along the x direction

Ox = AB + C'X = 4 +  4cos45 = 4 + 2√2 km

along the y direction

Oy = CX = 4sin45 = 2√2 km

the coordinates of the final position would be

(4 + 2√2, 2√2)