John D
This looks like a relativity question. The ball will land right in front of her, relative to her position on the moving train, but to a watcher along side the moving train, it will appear to move in an arc, since she is throwing it upwards, and the train is simultaneously moving forward.

pariah z
While the train (and the woman) slows down, the ball will more or less continue at a constant velocity- meaning that, relative to the woman, the ball will move forward in the air. The woman is sitting on the train, so her decelleration will be identical to that of the train's.

lilmaninbigpants
okay this is what will happen. Lets say at the instant she throws the ball up the train has horizontal velocity v. Given that there is no air resistance and other factors. The ball will maintain constant velocity, which is v in the horizontal direction. But since the train is slowing down the ball will overtake and fall somewhere in front of her.

raj
The ball will land infront of the woman. The velocity of the ball at the time of projection is equal to the velocity of the train, which is directed horizontal. Also it remains constant. As the train is slowing down the velocity of the train becomes less than that of the ball and hence the ball lands infront of the woman.