A) \[4h=3H\]
B) \[3h=4H\]
C) \[3h=H\]
D) \[4h=H\]
Correct Answer: A
Solution :
From the equation of motion \[{{v}^{2}}={{u}^{2}}+2as\] \[{{v}^{2}}-{{u}^{2}}=2as\] \[{{0}^{2}}-{{u}^{2}}=2\times (-g)\times H\] \[u=\sqrt{2gH}\] Now, \[h=ut-\frac{1}{2}g{{t}^{2}}\] \[h=(\sqrt{2gH})t-\frac{1}{2}g{{t}^{2}}\] This equation is quadratic in t. Solve for t we get, values for time. Ratio is \[\frac{{{t}_{1}}}{{{t}_{2}}}=\frac{1}{3}\] (given) substituting values, we get \[4h=3H\]
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