Answer to Question #140537 in Physics for Johnrheyl

Question

Do what is asked. Organize solutions properly (Given, Required, Solution). Express final
answer in complete statement, and in correct number of significant figures.
1. Below are three example displacement vectors. Add these displacement vectors to find the
resultant displacement. Use both graphical and analytical method in solving. Compare
results.
A= 10.0 m, 30º
B= 5.0 m, north
C= 12.0 m, 40º east of north

Answer 1

Given:

A= 10.0 m, 30º

B= 5.0 m, north

C= 12.0 m, 40º east of north

Required:

Find A+B+C graphically and analytically

Solution (analytical):

First, find the components of the vectors:

$$A_x=10\text{ cos}30°=8.66\text{ m},\\ A_y=10\text{ sin}30°=5\text{ m},\\ A=8.66i+5j.\\ B_x=5\text{ cos90}°=0,\\ B_y=5\text{ sin}90°=5\text{ m},\\ B=0i+5j.\\ C_x=12\text{ sin}40°=7.71\text{ m},\\ C_y=12\text{ cos}40°=9.19\text{ m},\\ C=7.71i+9.19j.$$

The resultant vector is

$$D=D_xi+D_yj=A+B+C=\\=8.66i+5j+0i+5j+7.71i+9.19j=\\=(16.37i+19.19j)\text{ m},\\ |D|=\sqrt{D_x^2+D_y^2}=25.2\text{ m},\\ \theta=\text{atan}\frac{19.19}{16.37}=49.5°.$$

Solution (graphical):

If we measure the angle and length of the resultant vector, we get approximately 25 m and 50°.