Why do ballistic missiles follow a high arcing flight path?

Ballistic missiles follow a high, arcing flight path because they are rocket-powered only during their initial boost phase. During this phase, the rocket engine provides the precise propulsion required to place the missile on a specific trajectory.123

Once the engine shuts off, the missile—or its payload—becomes unpowered and travels by momentum alone. From this point forward, the flight path is determined by the laws of physics, specifically the influence of gravity. The missile coasts through its midcourse phase, often traveling beyond the Earth’s atmosphere, before gravity pulls the warhead back down toward the target during the terminal phase.43152

Unlike cruise missiles, which are sustained along a low, level flight path by continuous engine power and aerodynamic lift, ballistic missiles rely on this initial burst of power to achieve the velocity and heading necessary to reach their target along a purely ballistic, arcing trajectory.13