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 $$t_2$$.

We have a ball released from rest at height $$h$$. Let $$t_1$$ be the time to cover the first half of the distance ($$h/2$$) and $$t_2$$ be the time to cover the second half.

The total time to fall a distance $$h$$ from rest is given by $$h = \frac{1}{2}g T^2$$, so $$T = \sqrt{\frac{2h}{g}}$$.

Now the time to fall the first $$h/2$$ is $$\frac{h}{2} = \frac{1}{2}g t_1^2$$, giving $$t_1 = \sqrt{\frac{h}{g}}$$.

We can write $$T = \sqrt{\frac{2h}{g}} = \sqrt{2} \cdot \sqrt{\frac{h}{g}} = \sqrt{2}\, t_1$$.

Since $$T = t_1 + t_2$$, we get $$t_2 = T - t_1 = \sqrt{2}\, t_1 - t_1 = (\sqrt{2} - 1)\, t_1$$.

Hence, the correct answer is Option 4.