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

Options

A. Straight line path
B. Circular path
C. Parabolic path
D. Hyperbolic path

Explanation

To solve the problem of a stone released from a moving train, we need to analyze the motion of the stone in both horizontal and vertical directions.

### Step-by-Step Solution:

1. **Understand the Situation**:
- A stone is released from a window of a train that is moving horizontally with a certain velocity \( v \).
- The stone will initially have the same horizontal velocity as the train at the moment of release.

2. **Identify the Forces Acting on the Stone**:
- Once the stone is released, the only force acting on it is gravity, which acts downwards with an acceleration of \( g \) (approximately \( 9.81 \, \text{m/s}^2 \)).
- There are no horizontal forces acting on the stone after it is released.

3. **Horizontal Motion**:
- The horizontal velocity of the stone \( v_h \) remains constant and is equal to the velocity of the train \( v \).
- The stone will continue to move horizontally with this velocity until it hits the ground.

4. **Vertical Motion**:
- The stone starts from rest in the vertical direction (initial vertical velocity \( u_y = 0 \)).
- It will accelerate downwards due to gravity, following the equation of motion:
\[ y = u_y t + \frac{1}{2} g t^2 \]
- Since \( u_y = 0 \), the equation simplifies to:
\[ y = \frac{1}{2} g t^2 \]

5. **Path of the Stone**:
- The stone will follow a parabolic trajectory because it has a constant horizontal velocity and is accelerating downwards.
- The horizontal distance traveled can be expressed as:
\[ x = v_h t = v t \]
- Combining the horizontal and vertical motions, the path traced by the stone will be a parabola.

6. **Conclusion**:
- The stone will hit the ground following a parabolic path due to the combination of its constant horizontal motion and the vertical acceleration due to gravity.

### Final Answer:
The stone will hit the ground following a parabolic path.