A) \[{{\tan }^{-1}}\left( \frac{3}{2} \right)\]
B) \[{{\tan }^{-1}}\left( \frac{2}{3} \right)\]
C) \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]
D) \[{{\tan }^{-1}}\left( \frac{3}{4} \right)\]
Correct Answer: B
Solution :
We know that range of a projectile \[R=\frac{{{U}^{2}}\sin 2\theta }{g}\] Here \[R=6+18=24\] \[\therefore \] \[\frac{{{u}^{2}}\sin 2\theta }{g}=24\] ? (i) The equation of trajectory of a projectile \[y=x\tan \theta -\frac{g{{x}^{2}}}{2{{U}^{2}}{{\cos }^{2}}\theta }\] \[3=6\tan \theta -\frac{36g}{2{{U}^{2}}{{\cos }^{2}}\theta }\] ? (ii) Form Eq. (i), \[\frac{g}{{{U}^{2}}}=\frac{\sin 2\theta }{24}\] \[=\frac{\sin \theta \cos \theta }{12}\] Substituting in Eq. (ii), we get \[3=6\tan \theta -\frac{3}{2}\] \[\tan \theta =\frac{9}{2}\tan \theta \] \[\Rightarrow \] \[\theta ={{\tan }^{-1}}\left( \frac{2}{3} \right)\]You need to login to perform this action.
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