Answer
R= 2.81 Km
$\theta $ = $38.5^{\circ}$ North of West
Work Step by Step
Given
Let A= 3.25 KM
B= 2.20 Km
C= 1.5 Km
So let us calculate the components of vectors
Ax=0
Ay=3.25 Km
Bx=-2.20, Km ( Here the singe negative - cause the x- components lies in the -ve x-directions )
By=0
Cx=0
Cy=-1.50 km
=> R ⃗=A ⃗+B ⃗+C ⃗
So now by using the component method of adding vectors :
Rx = Ax+ Bx+ Cx
Rx= 0 - 2.20 - 0
= -2.20 Km
Ry= Ay+By+ Cy
=-3.25 +0 -1.50
= 1.75 Km.
So, Now
To find the magnitude of R ⃗ :
R=$4\sqrt R\frac{2}{yx} +R \frac{2}{y}$
R=$\sqrt (-2.20)^{2} + 1.75^{2}$
= 2.81 Km
To find the direction of R ⃗;
We must use the following equation
$ tan \theta = \frac{Ry}{Rx} $
$\theta4=tan^{-1} (\frac{1.75}{-2.20})$
=$ 38. 5^{\circ} North of west $
From the signs of Rx and Ry
R ⃗ lies in the second quadrant.
So the angle counterclockwise from the +x-axis
β=$ 180^{\circ} - 38.5^{\circ}$
= $141.5^{\circ}$
The resident displacement in the above-given diagram in qualitative agreement with the result calculated using the method of components.
