A person is sitting in a travelling train and facing the engine. He tosses up a coin and the coin falls behind him. It can be concluded that the train is

Options

A. forward and gaining speed.
B. forward and losing speed
C. backward and losing speed
D. backward and gaining speed

Explanation

To solve the problem, we need to analyze the situation of a person tossing a coin in a moving train. Here’s a step-by-step breakdown of the reasoning:

### Step 1: Understand the scenario
A person is sitting in a train that is moving forward and tosses a coin straight up. The coin falls behind him.

### Step 2: Analyze the motion of the coin
When the person tosses the coin, it initially has the same forward velocity as the train and the person. If the coin falls behind the person, it means that the train is moving faster than the coin after it has been tossed.

### Step 3: Establish the velocities
- Let \( V_t \) be the velocity of the train.
- When the coin is tossed, it has an initial velocity equal to \( V_t \) (the same as the train).
- After being tossed, the coin will experience a downward acceleration due to gravity, which will affect its vertical motion but not its horizontal motion.

### Step 4: Determine the relative motion
Since the coin falls behind the person, it indicates that the train is either:
1. Moving forward and gaining speed, or
2. Moving forward and losing speed.

However, if the train were losing speed, the coin would not fall behind the person; it would fall in line with or ahead of him because the train would be decelerating.

### Step 5: Conclusion
Since the coin falls behind the person, it can be concluded that the train is moving forward and gaining speed.

### Final Answer
The correct conclusion is that the train is moving forward and gaining speed.

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