The sum of the magnitudes of two forces acting at point is $$18$$ and the magnitude of their resultant is $$12$$. If the resultant is $$at900$$ with the force of smaller magnitude, what are the magnitudes of forces ?

Question

The sum of the magnitudes of two forces acting at point is $$18$$ and the magnitude of their resultant is $$12$$. If the resultant is $$at900$$ with the force of smaller magnitude, what are the magnitudes of forces ?

Infinity Learn · Accepted Answer

Let P be the smaller force and Q be the greater force then according to $$problemP+Q$$ $$=$$ $$18$$       $$-----(i)R$$ $$=$$ $$P2+Q2+2PQcos$$θ $$=$$ $$12$$ $$----(ii)$$$$tan$$ϕ $$=$$ Qsinθ$$P+Q$$ $$cos$$θ $$=$$ $$tan900$$ $$=$$ ∞∴ $$P+Q$$ $$cos$$θ $$=$$ $$0$$   $$---(iii)By$$ solving (i), (ii) and (iii) we will get P $$=$$ $$5$$, and Q $$=$$ $$13$$

The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at $90^{0}$ with the force of smaller magnitude, what are the magnitudes of forces ?

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The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at900 with the force of smaller magnitude, what are the magnitudes of forces ?

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The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at $90^{0}$ with the force of smaller magnitude, what are the magnitudes of forces ?