Forces 90N and 120N act in the directions 120° and 240° respectively. Find the resultant of these forces.
-
A.
(-45(2i + sqrt{2}j)) -
B.
(60(sqrt{3}i + 7j)) -
C.
(30(7i + sqrt{3}j)) -
D.
(-15(7i + sqrt{3}j))
Correct Answer: Option D
Explanation
(F = Fcostheta + Fsintheta)
(implies 90N = 90cos 120° + 90sin 120°)
(120N = 120 cos 240° + 120 sin 240°)
(R = F_{1} + F_{2} )
= ((90 cos 120 + 120 cos 240)i + (90sin 120 + 120 sin 240)j)
= (90(-0.5) + 120(-0.5))i + (90(frac{sqrt{3}}{2}) + (120(-frac{sqrt{3}}{2}))j)
= (-105i – 15sqrt{3}j = -15(7i + sqrt{3}j))