Question #243415

F1 = 40N, 30º SE; F2 = 25N, 40º NW; and F3 = 30N, 50º NE, what is the resultant vector R?


1
Expert's answer
2021-09-29T00:27:39-0400
F1=(40sin(180°30°),40cos(180°30°))F_1=(40\sin(180\degree-30\degree), 40\cos(180\degree-30\degree))

F2=(25sin(40°),25cos(40°))F_2=(25\sin(-40\degree), 25\cos(-40\degree))

F3=(30sin(50°),30cos(50°))F_3=(30\sin(50\degree), 30\cos(50\degree))

R=F1+F2+F3R=F_1+F_2+F_3

=(40sin(150°)25sin(40°)+30sin(50°),=(40\sin(150\degree)-25\sin(40\degree)+30\sin(50\degree),

40cos(150°)cos(40°)+30cos(50°))40\cos(150\degree)-\cos(40\degree)+30\cos(50\degree))

(26.911643,34.508499)\approx(26.911643, -34.508499)

R=(26.911643)2+(34.508499)2|R|=\sqrt{(26.911643)^2+(-34.508499)^2}

=43.76 N=43.76\ N

tanθ=34.50849926.911643\tan \theta=\dfrac{-34.508499}{26.911643}

θ=52.05°\theta=-52.05\degree

R=43.76 N,37.95ºSER = 43.76\ N, 37.95º SE


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