Question Stem
A projectile is thrown from a point O on the ground at an angle $$45^\circ$$ from the vertical and with a speed $$5\sqrt{2}$$ 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 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 $$g = 10 m/s^2$$.