# 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 $54.25^{\circ} ,\:North\:of\:West$