Question

2 equal foces of magnitude Xn act cocurrently at a point P with angle 'a' in between them. show that the resultant force is given by 2xcos(a/2)

Answer 1

The resultant of two vectors of magnitudes A and B is given by\[\sqrt{A ^{2}+B ^{2}+2AB \cos \theta}\]
We now have A=B=x
So\[\sqrt{x ^{2}+x ^{2}+2x ^{2} \cos \theta}\]
\[\sqrt{2x ^{2}+2x ^{2} \cos \theta}\]
\[\sqrt{2} \ x \ \sqrt{1+ \cos \theta}\]
\[\sqrt{2} \ x \ \sqrt{2 \ \cos ^{2} \theta / 2} \]
\[2 \ x \cos \theta/2\]