A train is approaching towards a stationary person with a velocity v . The train emits a light signal. The signal will reach the stationary person with a velocity

Options

A. c
B. c+v
C. c-v
D. `sqrt(c^(2) + v^(2))`

Answer

To solve the problem of how fast the light signal emitted from a moving train will reach a stationary person, we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- We have a train moving towards a stationary person with a velocity \( v \).
- The train emits a light signal.

2. **Velocity of Light**:
- The speed of light in a vacuum is denoted by \( c \), which is approximately \( 3 \times 10^8 \) m/s.
- This speed is constant and does not change regardless of the motion of the source emitting the light.

3. **Effect of the Train's Motion**:
- The train is moving towards the person, which means that the distance between the train and the person is decreasing.
- However, the speed of the light signal itself remains \( c \).
- The frequency of the light signal may change due to the Doppler effect (the train moving towards the observer increases the frequency), but the speed of light remains constant.

4. **Conclusion**:
- Since the speed of light is invariant and does not depend on the motion of the source, the light signal emitted by the train will reach the stationary person with a velocity of \( c \).

### Final Answer:
The light signal will reach the stationary person with a velocity of \( c \) (approximately \( 3 \times 10^8 \) m/s).

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