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Comparing Vectors

Two forces ma...

Question

Two forces make an angle of 60degree . The magnitude of one of the forces is 4N and that of the resultant is 6N . Find the magnitude of the other force.

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Solution

$M a g n i t u d e o f t h e f i r s t f o r c e = f_{1} = 4 N r e s u l \tan t = 6 N l e t s e c o n d f o r c e i s f_{2} a n g l e b e t w e e n f_{1} a n d f_{2} i s 60 d e g r e e R = \sqrt{{f_{1}}^{2} + {f_{2}}^{2} + 2 f_{1} f_{2} \cos θ} 6 = \sqrt{{f_{1}}^{2} + 16 + 8 f_{1} \cos 60} 36 = {f_{1}}^{2} + 16 + 4 f_{1} {f_{1}}^{2} + 4 f_{1} - 20 = 0 f_{1} = \frac{- 4 \pm \sqrt{16 + 80}}{2} f_{1} = \frac{- 4 \pm 9.7}{2} f_{1} = - 6.85 N o r 2.85 N$

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