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: } √(R_x^2+R_y^2) = 60m`

`\textbf{Direction of resultant: }{\tan^(-1){(R_y)/(R_x)}= 39^(\circ)` north of east