How do you do this?
A = 145 units @ 190o
B = 75 units @ 288o
C = 210 units @ 85o
D = 105 units @ 355o
Find the resultant vector:
R = A + B + C + D
add the vectors (assuming N, S, E, W vectors), and the angles are measured clockwise from N 000 .
A=145 (cos190 N + sin 190 E)
B=75 (cos288 N + sin 288 E)
and so on. Then add all the N components, and all the E components.
R=M @ angle
where M= sqrt (sum N components ^2 + sum E components^2)
and angle= arc tan Ecomponents/Ncomponents
Vector = magnitude (cos T i + sin T j )
i is x direction
j is y direction
Thus
R x component =
145 cos 190 + 75 cos 288 + 210 cos 85 + 105 cos 355
R y component = 145 sin 190 + 75 sin 288 etc
in the end
|R| = sqrt (Rx^2 + Ry^2)
angle = tan^-1 (Ry/Rx)
Note I assume x axis at 0
Bob used compass from N
To find the resultant vector, R, which is the vector sum of A, B, C, and D, we need to consider both the magnitudes and the directions of each vector.
1. Break down each vector into its horizontal and vertical components using trigonometry.
- For A:
Magnitude = 145 units
Angle = 190 degrees
Horizontal component of A = Magnitude * cos(Angle)
Vertical component of A = Magnitude * sin(Angle)
- For B:
Magnitude = 75 units
Angle = 288 degrees
Horizontal component of B = Magnitude * cos(Angle)
Vertical component of B = Magnitude * sin(Angle)
- For C:
Magnitude = 210 units
Angle = 85 degrees
Horizontal component of C = Magnitude * cos(Angle)
Vertical component of C = Magnitude * sin(Angle)
- For D:
Magnitude = 105 units
Angle = 355 degrees
Horizontal component of D = Magnitude * cos(Angle)
Vertical component of D = Magnitude * sin(Angle)
2. Add up the horizontal and vertical components separately to get the resultant components:
- Horizontal component of R = Sum of (Horizontal components of A, B, C, and D)
- Vertical component of R = Sum of (Vertical components of A, B, C, and D)
3. Calculate the magnitude and direction of the resultant vector:
- Magnitude of R = sqrt((Horizontal component of R)^2 + (Vertical component of R)^2)
- Angle of R = arctan((Vertical component of R) / (Horizontal component of R))
Let's apply these steps to find the resultant vector, R: