A ball is dropped by a passenger from the window of a train moving with uniform velocity. The ball will reach the ground following a

Options

A. parabolic path for the passenger
B. parabolic path for the man standing on the road .
C. straight line path for the passenger
D. straight line path for the man standing on the road

Answer

To solve the problem, we need to analyze the motion of the ball dropped from a moving train. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Initial Conditions
When the ball is dropped from the window of a train moving with uniform velocity, it initially has the same horizontal velocity as the train. Let’s denote the speed of the train as \( V_t \).

**Hint:** Remember that objects in motion retain their velocity unless acted upon by an external force.

### Step 2: Analyze the Motion of the Ball
As the ball is dropped, it will continue to move horizontally with the same velocity \( V_t \) (the velocity of the train) while simultaneously accelerating downwards due to gravity. The downward acceleration is \( g \).

**Hint:** Consider the independence of horizontal and vertical motions in projectile motion.

### Step 3: Determine the Path of the Ball
From the perspective of a passenger in the train, the ball appears to fall straight down because both the passenger and the ball are moving horizontally at the same speed \( V_t \). Therefore, the ball follows a straight-line path downwards from the window.

**Hint:** Think about how the observer's frame of reference affects the perceived motion of the ball.

### Step 4: Consider the Perspective of an Outside Observer
For an observer standing on the ground, the ball will appear to follow a parabolic trajectory. This is because the ball has a constant horizontal velocity \( V_t \) while it is also accelerating downwards due to gravity. The combination of these two motions results in a parabolic path.

**Hint:** Recall the equations of motion for both horizontal and vertical components to visualize the trajectory.

### Step 5: Conclusion
Based on the analysis:
- For the passenger in the train, the ball follows a straight-line path (downwards).
- For an observer on the ground, the ball follows a parabolic path.

Thus, the correct answer to the question is that the ball will reach the ground following a straight-line path from the perspective of the passenger in the train.

**Final Answer:** The ball will reach the ground following a straight-line path (Option C).

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