Passenger of a train just drops a stone from it. The train was moving with constant velocity. What is path of the stone as observed by (a) the passenger itself, (b) a man standing on ground?

Explanation

To solve the problem, we need to analyze the motion of the stone from two different reference frames: that of the passenger on the train and that of a man standing on the ground.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- The train is moving with a constant velocity \( u \) horizontally.
- A passenger drops a stone from the train.

2. **Analyzing the Motion from the Passenger's Frame**:
- When the passenger drops the stone, it has the same horizontal velocity \( u \) as the train at the moment of release.
- Since the passenger is also moving with the train, they perceive the stone to fall straight down.
- Therefore, the path of the stone as observed by the passenger is a **vertical line**.

3. **Analyzing the Motion from the Ground Frame**:
- For a man standing on the ground, the stone initially has a horizontal velocity \( u \) (the same as the train).
- As the stone falls, it is acted upon only by gravity, which causes it to accelerate downwards with an acceleration \( g \).
- The stone will move horizontally while simultaneously falling vertically, resulting in a **parabolic trajectory**.
- Thus, the path of the stone as observed by the man on the ground is a **projectile motion**.

### Summary of Results:
- (a) The path of the stone as observed by the passenger is **vertical**.
- (b) The path of the stone as observed by the man standing on the ground is **projectile motion** (a parabolic path).