Consider four vectors F1, F2, F3, and F4 with magnitudes F1= 44 N, F2= 31 N, F3=

Question

Consider four vectors F1, F2, F3, and F4 with magnitudes F1= 44 N, F2= 31 N, F3=12 N, F4= 66, theta1= 140o, theta2= -150o, theta3= 19o, and theta4= -75o, measured from the positive x axis with counterclockwise positive.

A) What is the magnitude of the resultant vector F= F1+ F2+ F3+ F4?

B) What is the direction of this resultant vector F, within the limits of -180o and 180o as measured from the postive x axis with counterclockwise positive? Answer in units of degrees.

I figured out part A is 56.9805 N, but I can't figure out part B.

Explanation / Answer

A) Fx = F1x + F2x + F3x + F4x

Fx = (44*cos140)+(31*cos150)+(12*cos19)+(66*cos75)

Fx = -33.7 -26.84 + 11.34 + 17.08 = -32.12 N

Fy = (44*sin140)+(31*sin-150)+(12*sin19)+(66*sin-75) =

Fy = 28.28 - 15.5 + 3.9 - 63.75 = -47.07 N

F = 56.9805 N

B) direction = -124

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