Find the angle between forces of magnitude 7N and 4N if t...
Find the angle between forces of magnitude 7N and 4N if their resultant has a magnitude of 9N.
39.45°
73.40°
75.34°
106.60°
Correct answer is B
F1=7i+0j
F2=(4cosθ)i+(4sinθ)j
9=√(7+4cosθ)2+(4sinθ)2
92=(7+4cosθ)2+(4sinθ)2⟹81=49+56cosθ+16cos2θ+16sin2θ
81=49+56cosθ+16(cos2θ+sin2θ)
Recall, cos2θ+sin2θ=1
81=49+56cosθ+16⟹81−49−16=56cosθ
16=56cosθ⟹cosθ=1656=0.2857
\theta = \cos^{-1} 0.2857 = 73.40°
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