JEE Advanced 2021 Paper 1

Paragraph for next 2 questions A projectile is thrown from a point $O$ on the ground at an angle $45^{\circ}$ from the vertical and with a speed $5\sqrt{2}\,\text{m/s}$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, $0.5\,\text{s}$ 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 $g=10\,\text{m/s}^2$