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Grade 12th passVectors

Two forces P and 2P acting at a point have a resultant R which is perpendicular to the line P, find the angle between the forces.

Shams Ishtiaque Rahman

9 Years agoGrade 12th pass

1 Answer

Eshan

8 Years ago

The resultant of vectors $\vec{A}$ and $\vec{B}$ (with angle $\theta$ between them) forms an angle $\alpha$ with $\vec{A}$ such that

$tan\alpha=\dfrac{Bsin\theta}{A+Bcos\theta}$

Since $\alpha=90^{\circ}$ ,

$A+Bcos\theta=0\implies cos\theta=-\dfrac{A}{B}=-\dfrac{P}{2P}=-\dfrac{1}{2}$

$\implies \theta=120^{\circ}$

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