This animation shows another way of looking at the projectile problem in terms of Galilean Relativity.

The sailboat is an inertial reference frame, moving at constant horizontal velocity relative to the earth frame.

In the frame of the sailboat the projectile falls straight down, whereas in the earth's frame

it has a horizontal component of velocity equal to the velocity of the sailboat.

Clearly the height of the ball at any given time has to be the same in both reference frames.