(c) A force vector with a magnitude of 44 lb that is in the third quadrant with an x component whose magnitude is 38 lb.
find magnitude and angle
To find the magnitude and angle of the force vector, we can use trigonometry.
First, let's visualize the force vector in the third quadrant. In the third quadrant, the x and y components of the vector are both negative.
Given:
Magnitude of the force vector (|F|) = 44 lb
Magnitude of the x component (|F_x|) = 38 lb
To find the magnitude of the y component (|F_y|), we can use the Pythagorean theorem:
|F|^2 = |F_x|^2 + |F_y|^2
44^2 = 38^2 + |F_y|^2
1936 = 1444 + |F_y|^2
|F_y|^2 = 1936 - 1444
|F_y|^2 = 492
|F_y| = √492
|F_y| ≈ 22.18 lb
Now, we have the magnitudes of the x and y components. To find the magnitude of the force vector, we can use the Pythagorean theorem again:
|F|^2 = |F_x|^2 + |F_y|^2
|F|^2 = 38^2 + 22.18^2
|F|^2 = 1444 + 491.7124
|F|^2 = 1935.7124
|F| ≈ √1935.7124
|F| ≈ 43.96 lb
The magnitude of the force vector is approximately 43.96 lb.
To find the angle, we can use the inverse tangent function:
θ = tan^(-1)(|F_y| / |F_x|)
θ = tan^(-1)(22.18 / -38)
θ ≈ -30.26°
Therefore, the magnitude of the force vector is approximately 43.96 lb and the angle is approximately -30.26°.