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Q.
A ball is released from a height $h$. If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$.
For first $\frac{ h }{2}$
$\frac{ h }{2}=\frac{1}{2} gt _1^2$
For total height $h$
$ h =\frac{1}{2} g \left( t _1+ t _2\right)^2$
$ \frac{1}{\sqrt{2}}=\frac{ t _1}{ t _1+ t _2}$
$ 1+\frac{ t _2}{ t _1}=\sqrt{2} $
$\frac{ t _1}{ t _2}=\frac{1}{\sqrt{2}-1}$
$ t _2=(\sqrt{2}-1) t _1$