# Vector Displacement| Vector Addition and Subtraction: Graphical Method| Two-Dimensional Kinematics| College Physics Problem 3.4

### Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B, as in Figure 3.55, then this problem asks you to find their sum R = A + B .)




SOLUTION:

Refer to the diagram

The magnitude of the displacement (distance from the starting point to the final position) is given by

$R=\sqrt{A^2+B^2}$

$R=\sqrt{\left(18.0\:m\right)^2+\left(25.0\:m\right)^2}$

$R=30.8\:m$

The compass direction of a line connecting your starting point to your final position is given by

$\theta =tan^{-1}\left(\frac{B}{A}\right)$

$\theta =tan^{-1}\left(\frac{25.0\:m}{18.0\:m}\right)$

$\theta =54.25^{\circ}$

The compass reading is $54.25^{\circ} ,\:North\:of\:West$