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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 $t_{2}$.
Explanation
From equation of motion, $s = ut + \frac{1}{2}g^{2}$ For first $h/2$, $h/2 = \frac{1}{2}gt_{1}^{2}$ For total height h, $h = \frac{1}{2}g(t_{1} + t_{2})^{2}$ Divide equation (ii) by (i) we have $\frac{1}{2} = t_{1}^{2}/(t_{1}+t_{2})^{2}$ $1/\sqrt{2} = t_{1}/(t_{1} + t_{2})$; $1 + t_{2}/t_{1} = \sqrt{2}$ $t_{1}/t_{2} = 1/(\sqrt{2} - 1) \Rightarrow t_{2} = (\sqrt{2} - 1)t_{1}$