A girl drops an apple from the window of a train which is moving on a straight track with speed increasing with a constant rate. The trajectory of the falling apple as seen by the girl is:
A. parabolic and in the direction of the moving train.
B. parabolic and opposite to the direction of the moving train.
C. an inclined straight line pointing in the direction of the moving train.
D. an inclined straight line pointing opposite to the direction of the moving train.

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Hint: Check the direction and velocity of the apple when dropped from the window of the train by the girl. Hence, determine the net acceleration acting on the apple dropped which gives the direction of motion of the apple. Also consider the speed of the train. From all this information, determine the path of motion of the apple as seen by the girl in the train.

Complete answer:
We have given that the girl drops an apple from the window of a train and the train is moving on a straight track with speed increasing at a constant rate.Hence, the acceleration of the train is uniform.When the girl drops an apple out of the window of the train, the apple moves with the same velocity as that of the train at the instant when the apple was dropped. The apple continues its motion in the same direction as that of the train with the same instantaneous velocity. Hence, the acceleration of the apple is zero during its motion.

The acceleration acting on the apple is the acceleration due to gravity in the downward direction and due to this downward acceleration, the apple starts decelerating in the straight horizontal direction and starts falling down but not in the straight downward direction. The apple starts falling down making an angle with the horizontal in the straight line.

But the velocity of the train is increasing at a constant rate. Hence, the train moves ahead of the apple and the girl can see the apple falling down with an inclined angle with straight path of the train in the opposite direction as that the train.Therefore, the trajectory of the falling apple as seen by the girl is an inclined straight line pointing opposite to the direction of the moving train.

Hence, the correct option is D.

Note:The students may think that the path of the apple should be parabolic and not in the straight line. But the resultant of the deceleration of the apple and acceleration due to gravity is in the straight line in the direction opposite to the direction of the train. Hence, the apple is moving in a straight line and not in the parabolic path.