Answer to Question #138001 in Physics for Myca cemini

Question

A postal employee drives a delivery truck along the routes shown on the fogure. Determine the magnitude and direction of the resultant displacement by drawing a scale diagram

Answer 1

Since there is no figure attached, consider a typical problem:

We see the distances, we see the yellow total displacement vector AE. We can use Pythagorean theorem to find the magnitude. First, find displacement in the horizontal direction:

$$d_x=-9+3=-6\text{ km}$$

(it is negative because we imply normal notation where positive x looks to the right).

The displacement in the vertical direction:

$$d_y=13+5=18\text{ km},\\ d=\sqrt{d_x^2+d_y^2}=\sqrt{6^2+18^2}=19\text{ km},\\ \theta=\text{atan}\frac{-18}{3}=-72°.$$

72° above the horizontal "backwards" relative to initial direction AB.