A) \[(R+H),\,\frac{H}{2}\]
B) \[\left( R+\frac{H}{2} \right),\,\,2H\]
C) \[\left( R+2H \right),\,\,H\]
D) \[\left( R+H \right),\,\,H\]
Correct Answer: D
Solution :
\[R\,\,=\,\,\,{{u}_{x}}t+\frac{1}{2}\,\,{{a}_{x}}{{t}^{2}}\] \[=\,\,u\,\cos \theta \,\,\times \,\,\frac{2u\,\sin \,\theta }{g}\,\,+\,\,\frac{1}{2}\,\,\left( \frac{g}{4} \right)\,\,{{\left( \frac{2u\,\sin \,\theta }{g} \right)}^{2}}\] \[=\,\,\frac{2{{u}^{2}}\sin \,\theta \,\cos \,\theta }{g}\,\,+\,\,\frac{{{(u\,sin\,\theta )}^{2}}}{2g}\] \[=\,\,R\,\,+\,\,H,\,\,R\,\,\,\,=\,\,\,\frac{2{{u}^{2}}\,\sin \,\theta \,\cos \,\theta }{g}\] \[H\,\,=\,\,\frac{{{(u\,\sin \,\theta )}^{2}}}{2g}\]
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