(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.
To determine the y component of the force vector, we can use the knowledge that the force vector is in the third quadrant. In this quadrant, both the x and y components of the vector are negative.
Given:
Magnitude of the force (F) = 44 lb
Magnitude of the x component (Fx) = 38 lb
To find the magnitude of the y component (Fy), we can use the Pythagorean theorem:
F^2 = Fx^2 + Fy^2
Rearranging the equation to solve for Fy:
Fy^2 = F^2 - Fx^2
Fy^2 = (44 lb)^2 - (38 lb)^2
Calculating:
Fy^2 = 1936 lb^2 - 1444 lb^2
Fy^2 = 492 lb^2
Taking the square root of both sides:
Fy = √492 lb
Fy ≈ 22.18 lb
Therefore, the magnitude of the y component of the force vector is approximately 22.18 lb.