A projectile is thrown from a point O on the ground at an angle 45^o from the vertical and with a speed $5\sqrt{2}$m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down 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 g =10 m/s².