A) \[\frac{2{{u}^{2}}}{5g}\]
B) \[\frac{3{{u}^{2}}}{5g}\]
C) \[\frac{{{u}^{2}}}{g}\]
D) \[\frac{{{u}^{2}}}{5g}\]
E) \[\frac{4{{u}^{2}}}{5g}\]
Correct Answer: E
Solution :
Maximum height \[=Range\times \frac{1}{2}\] \[\frac{{{u}^{2}}{{\sin }^{2}}\theta }{2g}=\frac{{{u}^{2}}\sin 2\theta }{g}\times \frac{1}{2}\] \[\frac{{{\sin }^{2}}\theta }{2}=\frac{2\sin \theta .\cos \theta }{2}\] \[\tan \theta =2\] \[\therefore \] \[\sin \theta =\frac{2}{\sqrt{5}}and\,\cos \theta =\frac{1}{\sqrt{5}}\] \[\therefore \] \[R=\frac{2{{u}^{2}}\sin \theta .\cos \theta }{g}\] \[\frac{2{{u}^{2}}\times \frac{2}{\sqrt{5}}\times \frac{1}{\sqrt{5}}}{g}\] \[R=\frac{4{{u}^{2}}}{5g}\]You need to login to perform this action.
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