Step 1: Understanding the Question:
This problem falls under the topic of Time, Speed, and Distance, specifically focusing on "train problems." When a train crosses a point object like a pole, a tree, or a standing man, the distance it covers is equal to its own length. The challenge here lies in the units provided: the speed is in kilometers per hour (km/h), while the time is in seconds and the required distance is in meters.
Step 2 : Key Formulas and approach:
1. Speed Conversion: To convert km/h to m/s, multiply the speed by $\frac{5}{18}$.
2. Distance Formula: $\text{Distance} = \text{Speed} \times \text{Time}$.
3. Concept Rule: $\text{Length of Train} = \text{Distance covered while crossing a point object}$.
The approach involves converting the speed to the correct units first and then applying the basic distance formula.
Step 3 : Detailed Explanation:
First, we note the given speed of the train, which is $72 \text{ km/h}$. Since the time is given in seconds, we cannot use km/h directly. We must transform this into meters per second (m/s).
Using the conversion factor, $\text{Speed in m/s} = 72 \times \frac{5}{18}$. Dividing 72 by 18, we get 4. Then, $4 \times 5 = 20 \text{ m/s}$. This means the train travels 20 meters every single second.
The time taken to cross the pole is 20 seconds. During these 20 seconds, the train must move forward by its entire length to completely clear the pole.
We now apply the distance formula: $\text{Distance} = 20 \text{ m/s} \times 20 \text{ s}$.
Calculating the product, $20 \times 20 = 400$. Since the units are m/s and seconds, the result is in meters.
Therefore, the distance covered in 20 seconds is 400 meters, which by definition is the physical length of the train.
If the train were crossing a platform, we would have added the platform length to the train length, but since a pole has no significant length, the distance is purely the train's length.
Step 4 : Final Answer:
The length of the train is 400 meters, which corresponds to option (C).