CHAPTER 11. VECTORS 11.8
Secondly we find the magnitude of the horizontal component, Bx:
cos θ =
Bx
B
cos21, 8 ◦ =
Bx
5 , 385
Bx = (5,385)(cos53, 13 ◦)
= 5m
5 m
3 m
4 m
Step 4 : Determine the components of the resultant vector
Now we have all the components. If we addall the horizontal components
then we will have the x-component of the resultant vector,R�x. Similarly, we add
all the vertical components then we will have the y-component of the resultant
vector,R�y.
Rx = Ax+ Bx
= 5m + 3m
= 8m
Therefore,R�xis 8 m to the right.
Ry = Ay+ By
= 2m + 4m
= 6m
Therefore,R�yis 6 m up.
Step 5 : Determine the magnitude and direction of theresultant vector
Now that we have the components of the resultant, we can use the Theorem of
Pythagoras to determinethe magnitude of the resultant, R.
R^2 = (Rx)^2 + (Ry)^2
R^2 = (6)^2 + (8)^2
R^2 = 100
∴ R = 10m
