From the perspective of the passenger inside the train, who is moving at a constant velocity along with the train, the stone dropped from the window will appear to follow a vertical path directly downward. This is because the stone, once detached from the passenger's hand, continues to move with the same horizontal velocity as the train.
The stone's motion can be understood by separating it into its horizontal and vertical components. The horizontal component is unaffected by the drop since there are no horizontal forces acting on the stone (assuming no air resistance). Therefore, the stone will continue to move horizontally at the same velocity as the train.
However, in the vertical direction, the stone will experience the force of gravity acting downward. Gravity will cause the stone to accelerate vertically, but since the stone was initially at rest relative to the train, it will fall straight down from the passenger's perspective. The stone's vertical motion will follow a path that is a vertical line, perpendicular to the train's motion.
It's important to note that this is the apparent path of the stone as observed by the passenger inside the moving train. From an observer outside the train, who is stationary or moving at a different velocity, the stone would follow a parabolic trajectory due to the combined effects of its horizontal motion and the acceleration of gravity.