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A passenger in a train moving at an acceleration 'a', drops a stone from the window. A person, standing on the ground, by the sides of the rails, observes the ball following:

1. Vertically with acceleration \( \sqrt{g^{2}+a^{2}} \)
2. Horizontally with an acceleration \( \sqrt{g^{2}+a^{2}} \)
3. Along a parabola with acceleration \( \sqrt{g^{2}+a^{2}} \)
4. Along a parabola with acceleration 'g"

Correct answer: Along a parabola with acceleration 'g"

Solution

In the ground frame, the stone has an initial horizontal velocity equal to the train’s speed at the moment of release, while its vertical motion is governed only by gravity. Since horizontal acceleration is zero and vertical acceleration is g, the path is a parabola with acceleration g.

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