A) \[g\sqrt{{{t}_{1}}{{t}_{2}}}\]
B) \[\frac{g{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\]
C) \[\frac{g\sqrt{{{t}_{1}}{{t}_{2}}}}{2}\]
D) \[\frac{g\left( {{t}_{1}}+{{t}_{2}} \right)}{2}\]
Correct Answer: D
Solution :
In case of motion under gravity, time taken to go up is equal to the time taken to fall down through the same distance. Time of descent \[({{t}_{2}})=\] time of ascent \[({{t}_{1}})=\frac{u}{g}\] \[\therefore \]Total time of flight \[T={{t}_{1}}+{{t}_{2}}=\frac{2u}{g}\] \[\Rightarrow \] \[u=\frac{g({{t}_{1}}+{{t}_{2}})}{2}\]
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