A projectile is launched from the origin with speed $v$ at an angle $\theta$ from the horizontal. At the highest point in the trajectory, the projectile breaks into two pieces, $A$ and $B$, of masses $m$ and $2m$, respectively. Immediately after the breakup piece $A$ is at rest relative to the ground. Neglect air resistance. Which of the following sentences most accurately describes what happens next?

Since the breakup occurs at the highest point, the vertical velocity just before the breakup is zero. The vertical momentum is therefore also zero. After the breakup piece $A$ is at rest, and hence has zero vertical momentum, so by conservation of momentum piece $B$ must also have zero vertical momentum, and therefore zero vertical velocity. Since pieces $A$ and $B$ are falling from the same height with the same initial vertical velocity, they will hit the ground at the same time. The pieces differ only in their masses and in their horizontal velocities, but neither of these quantities affect the time of fall.