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A particle is projected with a speed \( u \) in air at angle \( \theta \) with the horizontal. The particle explodes at the highest point of its path into two equal fragments, one of the fragments moving up straight with a speed \( u \). The difference in time in which the two particle fall on the ground is (Assume it is at a height \( H \) at the time of explosion)
(A) \( \frac{2 u}{g} \)
(B) \( \frac{u}{g} \sqrt{u^{2}-2 g H} \)
(B) \( \frac{1}{2 g} \sqrt{u^{2}+2 g H} \)
(D) \( \frac{2}{g} \sqrt{u^{2}+2 g H} \)
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