Step 1: Understanding the Concept:
When a moving train passes a "point object" of negligible width (like a telegraph pole, a signal post, or a person standing still), the distance covered by the train to completely clear that object is exactly equal to its own physical length.
However, we must be very careful with the measurement units. The speed is given in kilometers per hour (km/h), but the time is given in seconds, and the answer choices are in meters. Before any calculation, we must convert the speed into meters per second (m/s) to ensure unit consistency. Failure to do this is the most common reason for errors in these problems.
Step 2: Key Formula or Approach:
1. Conversion Formula: To convert km/h to m/s, multiply by \(\frac{5}{18}\).
2. Distance Formula: \(\text{Distance} = \text{Speed} \times \text{Time}\).
3. Train length: In this context, \(\text{Length} = \text{Speed (m/s)} \times \text{Time (s)}\).
Step 3: Detailed Explanation:
Let's complete the calculations systematically in two main phases.
Phase A: Unit Transformation
The speed is 72 km/h. We need to convert this to m/s:
\[ \text{Speed} = 72 \times \frac{5}{18} \text{ m/s} \]
Dividing 72 by 18 gives exactly 4.
\[ \text{Speed} = 4 \times 5 = 20 \text{ m/s} \]
This means the train covers 20 meters every single second.
Phase B: Distance Calculation
The train takes 15 seconds to pass the stationary pole. This duration represents the time taken for the entire length of the train (from its front tip to its rear end) to pass the fixed point.
Using the distance formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ \text{Distance} = 20 \text{ m/s} \times 15 \text{ s} = 300 \text{ meters} \]
Since the total distance traveled while passing a single point is equal to the train's own span, the length of the train is 300 m.
Step 4: Final Answer:
The length of the train is 300 m, matching option (c).