The three displacement vectors in the drawing have magnitudes of A=4.30m,B=5.18m, and C=4.62m find the resultant (a) magnitude and (b) directional angle of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis which is less than 90 degree.
To find the resultant of the three displacement vectors using the component method, we need to break down each vector into its x and y components.
Let's denote the x component of vector A as A_x, the y component of vector A as A_y, and similarly for vectors B and C.
Given:
Magnitude of vector A (A) = 4.30 m
Magnitude of vector B (B) = 5.18 m
Magnitude of vector C (C) = 4.62 m
Using the component method, we can break down each vector into its x and y components using trigonometry.
For vector A:
A_x = A * cos(θ_A)
A_y = A * sin(θ_A)
For vector B:
B_x = B * cos(θ_B)
B_y = B * sin(θ_B)
For vector C:
C_x = C * cos(θ_C)
C_y = C * sin(θ_C)
Now, we need to find the values of θ_A, θ_B, and θ_C. The question does not provide information about the angles. We need the angles to calculate the components.
Without the angle values, we cannot determine the components or the resultant.
Please provide the values of θ_A, θ_B, and θ_C, or any additional information given in the question.