# Vector Addition and Subtraction| Two-Dimensional Kinematics| College Physics| Openstax| Problem 3.1|

#### Find the following for path A in Figure 3.54:           (a) The total distance traveled, and           (b) The magnitude and direction of the displacement from start to finish.

SOLUTION:

Part a

The total distance traveled is

$d=\left(3\times 120m\right)+\left(1\times 120\:m\right)$

$d=480\:m$

Part b

The magnitude of the displacement is

$s=\sqrt{s_x^{2\:}+s_y^2}$

$s=\sqrt{\left(1\times 120\:m\right)^2+\left(3\times 120\:m\right)^2}$

$s=379\:m$

The direction is

$\theta =tan^{-1}\left(\frac{s_x}{s_y}\right)$

$\theta =tan^{-1}\left(\frac{1\times 120\:m}{3\times 120m}\right)$

$\theta =71.6^{\circ} ,\:E\:of\:N$