A grenade is thrown with an initial speed of $300$ m$/$s in an angle of $45$ degree with the horizontal. When the grenade is at the vertex of its trajectory, explodes in two equal parts. If after the explosion, one of the pieces falls vertically without initial velocity, at what horizontal length from the throwing place falls the second piece? Find the position of the center of mass after explosion. Would it be different than the position of the center of mass if the explosion did n$$ot occur?