JEE Advanced 2021 — Paper 1 — Question 32

A projectile is thrown from a point $O$ on the ground at an angle $45^{\circ}$ from the vertical and with a speed $5 \sqrt{2} \mathrm{~m} / \mathrm{s}$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, t seconds after the splitting, falls to the ground at a distance x meters from the point O . The acceleration due to gravity $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$.

The value of $t$ is $\text{ }\!\!~\!\!\text{ }$