A) \[{{\tan }^{-1}}(2)\]
B) \[{{\tan }^{-1}}(4)\]
C) \[{{\tan }^{-1}}\left( \frac{1}{4} \right)\]
D) \[45{}^\circ \]
Correct Answer: B
Solution :
Maximum range\[R=\frac{{{u}^{2}}\sin 2}{g}\] Maximum height\[H=\frac{{{u}^{2}}{{\sin }^{2}}}{2g}\] Given \[R=H\] \[\Rightarrow \] \[\frac{{{u}^{2}}\sin \,2\,}{g}=\frac{{{u}^{2}}\sin {{\,}^{2}}}{2g}\] or \[\frac{{{u}^{2}}(2\sin \theta \,\cos \theta )}{g}=\frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}\] or \[2\,\cos \,\,\text{=}\frac{\sin \,}{2}\] or \[\frac{\sin \,}{\cos \,}=4or\,\tan \,\text{=}\,\text{4}\] \[\Rightarrow \] \[\,\text{=}\,{{\tan }^{-1}}(4)\]
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