A) \[\sqrt{8gh+{{g}^{2}}{{\left( \Delta \,t \right)}^{2}}}\]
B) \[\sqrt{8gh+{{\left( \frac{g\Delta \,t}{2} \right)}^{2}}}\]
C) \[\frac{1}{2}\sqrt{8gh+{{g}^{2}}{{\left( \Delta \,t \right)}^{2}}}\]
D) \[\sqrt{8gh+4{{g}^{2}}{{\left( \Delta \,t \right)}^{2}}}\]
Correct Answer: C
Solution :
\[\text{h=ut}-\frac{\text{1}}{\text{2}}\text{a}{{\text{t}}^{\text{2}}}\] \[\Rightarrow g{{t}^{2}}-2ut+2h=0\] Solving for t we get \[{{t}_{1}}+{{t}_{2}}=2u/g\] \[{{t}_{1}}\times {{t}_{2}}=2\,h\text{/}g\] \[\text{so, }\Delta \text{t= }\!\!|\!\!\text{ }{{t}_{1}}-{{t}_{2}}\text{ }\!\!|\!\!\text{ =}{{\left( {{t}_{1}}+{{t}_{2}} \right)}^{2}}-4{{t}_{1}}{{t}_{2}}\] Putting value we get \[\text{u=}\frac{1}{2}\sqrt{8hg+{{g}^{2}}\Delta {{t}^{2}}}\]
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