Center M and Linear Momentum?

In this kind of problems, air resistance is ignored. From your data, both fragments have the same vertical velocity (0), so they will reach ground at the same time (as well as the center of m). But the center of m moves as if no explosion took place (conservation of momentum) and reaches ground (umed flat) at distance d. First fragment drops directly, from top of trajectory, so it travels d/2. Since the center of m travels distance d, it follows that the second fragment travels distance 3d/2.