What type of missile is defined as being powered by rockets initially and then follows a free-falling trajectory?

A ballistic missile is characterized by its initial phase of being powered by rockets, which propel it into the upper atmosphere. Once this powered phase is complete, the missile follows a free-falling trajectory, propelled largely by gravity and aerodynamic forces rather than propulsion systems. This type of missile typically has a high arc during its flight path, reaching significant altitudes before descending toward its target.

In contrast, an improvised explosive device (IED) is an explosive weapon created and deployed in ways that are often informal or unconventional, and it does not follow a guided trajectory like a ballistic missile. Antiballistic missiles are designed to intercept and destroy ballistic missiles but do not follow the same trajectory themselves. Air-launched missiles are deployed from aircraft and typically remain guided throughout their flight, rather than transitioning to a free-falling state. Thus, the characteristics of the ballistic missile fit the definition provided, confirming that it is the correct answer.