The curved path of a projectile that accelerates only in the vertical direction while moving at a constant horizontal velocity is called a parabola.

Here's why:

* Gravity's Influence: The only force acting on the projectile after it's launched is gravity. This force pulls the projectile downwards, causing its vertical velocity to change.

* Constant Horizontal Velocity: The projectile's horizontal motion is unaffected by gravity. This results in a constant horizontal velocity.

* Combined Motion: The combination of constant horizontal velocity and changing vertical velocity creates a curved path. This path is mathematically described by a parabolic function.