A passenger at rest on a flatbed train car fires a bullet straight up. The event is viewed by observers at rest on the station platform as the train moves past the platform with constant velocity. What is the trajectory of the bullet as described by the observers on the platform?

Options

A. A straight horizontal path in the direction of the train's velocity.
B. A straight vertical path up and down.
C. A circular path centered on the gun.
D. A parabolic path.

Answer

To solve the problem, we need to analyze the motion of the bullet as observed from two different frames of reference: the passenger on the train and the observer on the platform.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- A passenger on a moving train fires a bullet straight up.
- The train is moving with a constant velocity \( v \) relative to the ground (station platform).
- The bullet is fired vertically upward from the passenger's perspective.

2. **Analyzing the Bullet's Motion**:
- From the passenger's perspective (inside the train), the bullet moves straight up and then comes straight back down due to gravity.
- From the platform observer's perspective, the bullet has two components of motion:
- **Vertical Component**: The bullet moves upward and then downward due to the force of gravity.
- **Horizontal Component**: Since the train is moving with a constant velocity \( v \), the bullet also has this horizontal velocity component.

3. **Combining the Components**:
- The bullet's trajectory can be described as a combination of the vertical motion (up and down) and the horizontal motion (moving forward with the train).
- The horizontal motion is uniform (constant velocity \( v \)), while the vertical motion is influenced by gravity (accelerating motion).

4. **Describing the Trajectory**:
- The overall trajectory of the bullet, as observed from the platform, will be a parabolic path. This is because the bullet moves upward and then downward while simultaneously moving horizontally due to the train's motion.

5. **Conclusion**:
- The trajectory of the bullet, as described by the observers on the platform, is a parabolic path.

### Final Answer:
The trajectory of the bullet as described by the observers on the platform is a parabolic path.