A shell is thrown vertically up. The shell at the highest point explodes into two equal fragments. The centre of mass of the two fragments

• The centre of mass of the two fragments' net horizontal velocity is 0. 
• Because gravity is the sole force working vertically downward after an explosion, the centre of mass falls to the ground. 
• Additionally, the centre of mass comes to rest at the highest point, hence the initial velocity of descent is zero.

Hence the correct answer is falls  down with zero inital velocity.