How far below an initial straight-line path will a projectile fall in one second

9.8 m

Explanation:

The rate of free fall of a body does not depend on its mass or shape in the absence of air resistance.  This property of gravitational force is proved by the famous leaning tower of Pisa experiment by Galileo.

The gravitational force is responsible for the gravitational acceleration of a body.

When considering the gravitational acceleration near the surface of Earth it has the constant value g = 9.8 m/s irrespective of the mass of the body.

This phenomenon states that every projectile falls at the same rate such that its velocity keeps on increasing to maintain the constancy of g.

So, when a projectile fall initially from a certain height for one second, it would have traveled only 9.8 m.