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.

Figure 3.54 The various lines represent paths taken by different people walking in a city. All blocks are 120 m on a side
Figure 3.54 The various lines represent paths taken by different people walking in a city. All blocks are 120 m on a side

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