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Physics · MOTION IN A PLANE
हिन्दीTwo forces of magnitudes 8 N and 15 N act at a point. If their resultant magnitude is 17 N, calculate the angle \( \theta \) between the two force vectors and the angle \( \beta \) that the resultant makes with the 8 N force.
Correct answer · Option 3
\( \theta = 90^\circ \), \( \beta = \tan^{-1}(\frac{15}{8}) \)
Explanation
Using \( R^2 = A^2 + B^2 + 2AB\cos\theta \implies 17^2 = 8^2 + 15^2 + 2(8)(15)\cos\theta \implies 289 = 289 + 240\cos\theta \implies \theta = 90^\circ \). The angle \( \beta \) with 8 N is \( \tan\beta = \frac{15\sin 90^\circ}{8 + 15\cos 90^\circ} = \frac{15}{8} \implies \beta = \tan^{-1}(15/8) \).
