JEE Advanced 2021 Paper 1

A projectile is thrown from a point O on the ground at an angle 45∘ from the vertical and with a speed 5√2m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5s 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=10m/s2