Question

Graphically determine the magnitude and direction of the
resultant of the following three vector displacements:
1. 15 m, 30° north of east
2. 20 m, 37° north of east
3. 25 m, 45 north of east

Answer 1

In in xy-plane, choose the +x-axis as east and the +y-axis as north

Then we can use the sum of the x-components and y-components to find the magnitude (using pythagoras) and direction (arctan)

sum of x-components:

$R_x=15\cos(30^{\circ})+20\cos(37^{\circ})+25\cos(45^{\circ})=46.64 \ m$

sum of y-components:

$R_y=15\sin(30^{\circ})+20\sin(37^{\circ})+25\sin(45^{\circ})=37.21m$

$\textbf{Magnitude of resultant: } \sqrt{R_x^2+R_y^2} = 60m$

$\textbf{Direction of resultant: }{\tan^{-1}{\frac{R_y}{R_x}}= 39^{\circ}$ north of east