Vector Barrowbold has magnitude 9.4 and direction 14° below the +x-axis. Vector Carrowbold has x-component Cx = -1.6 and y-component Cy = -7.7.
Compute direction of Carrowbold & direction of Carrowbold + Barrowbold.
Also direction of Carrowbold − Barrowbold and direction in ° counter-clockwise from the +x-axis!
Thnk you
C = -1.6 - i7.7. Q3.
tanAr = Y/X = -7.7 / -1.6 = 4.8125,
Ar = 78.3 Deg. =Reference angle.
A = 180 + Ar = 180 + 78.3 = 258.3 Deg.
B = 9.4 @ (-14) Deg. C = -1.6 -i7.7.
X = 9.4*cos(-)14 + (-1.6) = 7.52.
Y = 9.4*sin(-14) + (-7.7) = -9.97.
tanAr = Y/x = -9.97 / 7.52 = -1.3263,
Ar = -53 Deg.
A = -53 + 360 = 307 Deg.
C = -1.6 -i7.7. B = 9.4 @(-14) Deg.
X = -1.6 - 9.4*cos(-14) = -10.72.
Y = -7.7 - 9.4*sin(-14) = -5.43.
tanAr = Y/X = -5.43 / -10.72 = 0.5062.
Ar = 26.8 Deg.
A = 180 + 26.8 = 206.8 Deg.
To find the direction of a vector, we can use trigonometry. The direction of a vector is usually measured as the angle it makes with the positive x-axis, measured counterclockwise.
1. Direction of Carrowbold:
Given that the x-component of Carrowbold is Cx = -1.6 and the y-component is Cy = -7.7, we can use the inverse tangent function (arctan) to find the direction angle.
θ = arctan(Cy / Cx)
θ = arctan(-7.7 / -1.6)
θ ≈ 78.97°
Therefore, the direction of Carrowbold is approximately 78.97° counterclockwise from the +x-axis.
2. Direction of Carrowbold + Barrowbold:
To find the direction of the sum of two vectors, we can add their x-components and y-components separately, and then compute the resulting angle using the arctan function.
To add the two vectors, we first need to find the components of Barrowbold using magnitude and direction.
The x-component of Barrowbold can be found using cosine:
Bx = magnitude * cos(direction)
Bx = 9.4 * cos(14°)
Bx ≈ 9.168
The y-component of Barrowbold can be found using sine:
By = magnitude * sin(direction)
By = 9.4 * sin(14°)
By ≈ 2.393
Now, we can calculate the sum of the x-components and y-components of the two vectors:
Sum_x = Cx + Bx
Sum_y = Cy + By
Sum_x = -1.6 + 9.168 ≈ 7.568
Sum_y = -7.7 + 2.393 ≈ -5.307
Next, we find the direction angle of the summed vector:
θ_sum = arctan(Sum_y / Sum_x)
θ_sum = arctan(-5.307 / 7.568)
θ_sum ≈ -35.55°
Therefore, the direction of Carrowbold + Barrowbold is approximately -35.55° counterclockwise from the +x-axis.
3. Direction of Carrowbold - Barrowbold:
To find the direction of the difference of two vectors, we can subtract their x-components and y-components separately, and then compute the resulting angle using the arctan function.
Subtracting the components of Barrowbold from Carrowbold:
Diff_x = Cx - Bx
Diff_y = Cy - By
Diff_x = -1.6 - 9.168 ≈ -10.768
Diff_y = -7.7 - 2.393 ≈ -10.093
Now, we can calculate the direction angle of the difference vector:
θ_diff = arctan(Diff_y / Diff_x)
θ_diff = arctan(-10.093 / -10.768)
θ_diff ≈ 45.47°
Therefore, the direction of Carrowbold - Barrowbold is approximately 45.47° counterclockwise from the +x-axis.