A) \[{{\tan }^{-1}}\left( 2 \right)\]
B) \[\frac{\pi }{6}\]
C) \[\frac{\pi }{4}\]
D) \[{{\tan }^{-1}}\left( \frac{1}{2} \right)\]
Correct Answer: A
Solution :
Maximum height, \[{{H}_{0}}=\frac{{{u}^{2}}{{\sin }^{2}}\theta }{2\,g}\] Range, \[R=\frac{{{u}^{2}}\sin \,2\theta }{2\,g}\] Given, \[{{H}_{0}}=\frac{R}{2}\] \[\therefore \] \[\frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}=\frac{{{u}^{2}}\sin \theta \cos \theta }{2g}\] \[\Rightarrow \] \[\sin \theta =2\cos \theta \] \[\Rightarrow \] \[\tan \theta =2\] \[\therefore \] \[\theta ={{\tan }^{-1}}(2)\]
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