A) \[\sqrt{\left( {{a}^{2}}+1 \right)h}\]
B) \[\sqrt{{{a}^{2}}h}\]
C) \[\sqrt{ah}\]
D) \[2\sqrt{a(a+h)}\]
Correct Answer: D
Solution :
[d] Coordinates of point P are \[(R,-h)\]. Hence \[-h=R\tan \theta -\frac{g{{R}^{2}}}{2\left( 2ga \right)}\left( 1+{{\tan }^{2}}\theta \right)\] \[\Rightarrow \,\,\,\,{{R}^{2}}{{\tan }^{2}}\theta -4aR\,\,\tan \theta +({{R}^{2}}-4ah)=0\] For \[\theta \] to be real, \[{{(4aR)}^{2}}\ge 4{{R}^{2}}({{R}^{2}}-4ah)\] \[\Rightarrow \,\,\,4{{a}^{2}}\ge ({{R}^{2}}-4ah)\Rightarrow {{R}^{2}}\le 4a(a+h)\] \[\Rightarrow \,\,R\le 2\sqrt{a(a+h)}\,\,\,\,\,\Rightarrow \,\,\,\,\,\,{{R}_{\max }}=2\sqrt{a(a+h)}\]You need to login to perform this action.
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