A man A is sitting in the rear end of a long compartment of a train running at constant horizontal velocity, tosses a coin to a person B, near the front end of the compartment. The trajectory of the coin is, as seen by B and a person C on the ground, will have:

Options

A. different vertical ranges, but equal horizontal ranges
B. equal horizontal an equal vertical ranges
C. equal vertical ranges but different horizontal range
D. different vertical and different horizontal ranges

Explanation

To solve the problem of the trajectory of the coin tossed from person A to person B in a train compartment, we can analyze the situation step by step.

### Step 1: Understand the Frame of Reference
- **Situation**: Person A is at the rear end of a train compartment, and person B is at the front end. The train is moving with a constant horizontal velocity.
- **Frames of Reference**: There are two frames to consider:
1. The train's frame (where both A and B are at rest).
2. The ground frame (where the train is moving).

**Hint**: Identify the different frames of reference involved in the problem.

### Step 2: Analyze the Motion in the Train's Frame
- In the train's frame, when person A tosses the coin, it moves vertically upwards and downwards while also having a horizontal component due to the train's motion.
- Since the train is moving at a constant velocity, the horizontal motion of the coin will match the horizontal velocity of the train.

**Hint**: Consider the effects of the train's constant velocity on the motion of the coin.

### Step 3: Analyze the Motion in the Ground Frame
- In the ground frame, while the coin is tossed, it will have two components of motion:
1. **Vertical Motion**: The coin moves up and then down due to gravity.
2. **Horizontal Motion**: The coin also moves horizontally at the same speed as the train, which means it will continue to move forward as the train moves.

**Hint**: Break down the motion of the coin into horizontal and vertical components.

### Step 4: Combine the Motions
- The trajectory of the coin, as seen by person B (in the train), will appear as a straight vertical line (up and down).
- However, as seen by person C on the ground, the trajectory will be parabolic. This is because the coin moves forward while it is also going up and then coming down.

**Hint**: Visualize how the motion appears differently to observers in different frames.

### Step 5: Conclusion
- The trajectory of the coin, as observed by person B, is vertical.
- The trajectory of the coin, as observed by person C on the ground, is parabolic.

**Final Answer**: The trajectory of the coin will be vertical for person B and parabolic for person C.