A) \[\frac{3}{2}\]
B) \[\frac{3}{\sqrt{2}+1}\]
C) \[\frac{1}{\sqrt{2}-1}\]
D) \[\frac{5}{2}\]
Correct Answer: C
Solution :
For motion from \[P\] to \[Q\] \[y=\frac{1}{2}g{{t}_{1}}^{2}\] ? (1) For motion from \[P\] to\[R\]: \[2y=\frac{1}{2}g{{({{t}_{1}}+{{t}_{2}})}^{2}}\] ? (2) From (1) and (2), \[2{{t}_{1}}^{2}={{({{t}_{1}}+{{t}_{2}})}^{2}}\] \[\Rightarrow \] \[{{t}_{1}}+{{t}_{2}}=\sqrt{2}{{t}_{1}}\Rightarrow {{t}_{1}}\left( \sqrt{2}-1 \right)={{t}_{2}}\] \[\Rightarrow \] \[\frac{{{t}_{1}}}{{{t}_{2}}}=\frac{1}{\sqrt{2}-1}\]
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