A) \[\frac{v}{g}+\frac{2hg}{\sqrt{2}}\]
B) \[\frac{v}{g}\left[ 1-\sqrt{1+\frac{2h}{g}} \right]\]
C) \[\frac{v}{g}\left[ 1+\sqrt{1+\frac{2gh}{{{v}^{2}}}} \right]\]
D) \[\frac{v}{g}\left[ 1+\sqrt{{{v}^{2}}+\frac{2g}{h}} \right]\]
Correct Answer: C
Solution :
Since direction of v is opposite to the direction of g and h so from equation of motion \[h=-vt+\frac{1}{2}g{{t}^{2}}\] \[\Rightarrow g{{t}^{2}}-2vt-2h=0\] \[\Rightarrow t=\frac{2v\pm \sqrt{4{{v}^{2}}+8gh}}{2g}\] \[\Rightarrow t=\frac{v}{g}\left[ 1+\sqrt{1+\frac{2gh}{{{v}^{2}}}} \right]\]
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