A boy sitting on the topmost berth in the compartment of a train which is just going to stop on a railway station, drop an apple aiming at the open hand of his brother sitting vertically below his hands at a distnace of about 2 meter. The apple willl fall

Options

A. precisely on the hand of his brother
B. slightly away from the hand of his brother in the direction of motion of the train
C. Slightly away from the hand of his brother in the direction oppsite to the direction of motion on the train
D. none of above

Explanation

To solve the problem, we need to analyze the motion of the apple as it is dropped from the boy's hand in the train. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the scenario
The boy is sitting on the topmost berth of a train that is about to stop. He drops an apple aiming at his brother who is sitting directly below him, 2 meters away vertically.

### Step 2: Identify the initial conditions
When the boy drops the apple, it has the same horizontal velocity as the train because it is moving with the train at that moment. However, as the train begins to decelerate (retardation), the horizontal velocity of the boy (and thus the apple) will decrease.

### Step 3: Analyze the motion of the apple
1. **Vertical Motion**: The apple will fall under the influence of gravity. The vertical distance it needs to fall is 2 meters.
2. **Horizontal Motion**: The apple will continue to move horizontally at the initial velocity of the train when it is dropped. However, since the train is decelerating, the apple will not have the same horizontal displacement as the boy's brother.

### Step 4: Determine the effect of retardation
As the apple falls, the train will continue to slow down. This means that while the apple is falling straight down, it will also be moving horizontally at the initial speed of the train, but the boy (and the train) will be moving slower due to the retardation.

### Step 5: Conclusion
Since the apple retains its initial horizontal velocity while the boy (and the train) slows down, the apple will land slightly ahead of the brother's hand in the direction of the train's motion.

### Final Answer
The apple will fall slightly away from the hand of his brother in the direction of motion of the train.

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