Answer to Question #2805 in Mechanics | Relativity for noor

Question

A vector D = [ 30 cm , 50 degree ] and vector F = [ 45 cm , 150 degree ]
Use the graphic method to find the magnitude and direction of the sum R = D + F ?

Answer 1

In Cartesian coordinates
D={ρ₁ cosφ;ρ₁ sinφ} = {30*cos50;30*sin50} = {13.3;23}.
F={ρ₂ cosφ;ρ₂ sinφ} = {45*cos150;45*sin150} = {-39;22.5}.
D+F = {13.3-39;23+45.5} = {-25.7;45.5}.
The magnitude of vector is
M = √(-25.7² +22.5²) = 52.26 cm.
The same you can get depicting D as vector that originates at {0;0}, has length of 30 cm, angle between positive x direction is 50; and depicting F as vector that originates at {0;0}, has length of 45 cm, angle between positive x direction is 150