If a passenger sitting in a moving railway carriage throws a ball vertically upwards, the ball would fall in front of the passenger if the train is accelerating or moving at a constant speed.
When the ball is thrown upwards, it possesses an initial vertical velocity. However, both the passenger and the ball are also moving horizontally due to the motion of the train. If the train is accelerating or moving at a constant speed, the horizontal motion of the ball will be influenced by the forward motion of the train.
Since the ball and the passenger are moving horizontally at the same speed inside the train, the ball will retain its horizontal velocity when thrown vertically. However, due to the acceleration or constant speed of the train, the horizontal position of the passenger will change while the ball is in the air.
If the train is accelerating, the passenger's position will change, and the ball will fall in front of the passenger because the horizontal distance covered by the passenger during the ball's flight will be greater than the horizontal distance covered by the ball itself.
If the train is moving at a constant speed, there is no change in the passenger's horizontal position during the ball's flight. Thus, the ball will also fall in front of the passenger for the same reason as mentioned above—the horizontal distance covered by the passenger will be greater than the horizontal distance covered by the ball.
It's important to note that these observations assume no air resistance acting on the ball and neglect any effects due to wind or other external factors.