You walk 35 m south and 40 m east. Find the magnitude and direction of the resultant displacement both graphically and algebraically
When you walk 35 m south and 40 m east, the magnitude of your displacement is given by sqrt(35^2 + 40^2) = sqrt(1225+1600) = sqrt(2825) = 53.15 m
The angle of displacement is arc tan(40/35) = 48.81 degrees east of south.
The displacement is expressed graphically below. The start point is the origin. Green represents your movement towards the south. Then you move towards the east and the dark black line is your displacement.
The magnitude of displacement is 53.15 m and the direction is 48.81 degrees east of south.