Question

A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground in

Answer 1

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In order to understand the trajectory of a particle, we need to know both the x - axis and y - axis velocities of the particle.

Whenever we release a stone out of the window of a moving train , the stone has the following initial Velocity components :

• X - axis : similar to that of the train's Velocity
• Y - axis : Zero , as it is dropped.

As a result of this kind of Velocity profile , the stone performs a Height To Ground Projectile.

Considering the height of window of the train to be "h".

$h = ut + \frac{1}{2} g {t}^{2}$

$= > h = 0 + \frac{1}{2} g {t}^{2}$

$= > t = \sqrt{ \dfrac{2h}{g} }$

So final time taken :

$\boxed{ \green{ \huge{ \sf{ \bold{ t = \sqrt{ \dfrac{2h}{g} } }}}}}$

Answer 2

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The stone will follow the motion of a projectile, because of several reasons:

It has a initial horizontal velocity, which is same as that of the train .

It acquires  a vertical component under the force of gravity .

Since it has a constant speed on horizontal direction and a constant acceleration in vertical direction, the trajectory is parabolic.