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Paragraph: A projectile is thrown from a point \( \mathrm{O} \) on the ground
P at an angle \( 45^{\circ} \) from the vertical and with a speed \( 5 \sqrt{2} \mathrm{~m} / \mathrm{s} \).

W. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, \( 0.5 \mathrm{~s} \) 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 \( g=10 \mathrm{~m} / \mathrm{s}^{2} \).
The value of \( x \) is
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