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Sir,
the train is moving with a constt. speed and you are on the rooftop,you through a ball in upward direction will the ball come in your hand or it'll be left behind(in opposite direction of the train.)
At the time of releasing the ball, the ball, you and the train are all travelling in the horizontal direction at the same velocity, say v. Given that you throw the ball vertically upwards, you are not imparting any additional velocity to the ball along the orizontal direction. Hence, the relative velocity of the ball with respect to you along the horizontal direction is zero. Hence, the ball will come back in your hand.
THE BALL COME BACK TO YOUR HAND.
This is because before throwing the ball, the ball has the same velocity as the train and you as you all are moving with the same velocity as that of the train. Now when u leave the ball, the ball has a horizontal velocity v and an upward velocity u impart to it, SO it follows a parabolic path. Now since in the horizontal direction, there is no external force on you as well as that on the ball, u both have zero acc. in the horizontal direction , Hence the ball returns to your hand.
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