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 splitting, falls to the ground at a distance x meters from the point O. The acceleration due to gravity g = 10 m/s2. The value of t is $\underline{\hspace{2cm}}$.