Two trains cross each other at speeds of `36 km//h` and `54 km//h` travelling in the opposite directions in 2 sec. What is the length of the second train (in km)?

Explanation

To find the length of the second train, we can follow these steps:

### Step 1: Convert the speeds from km/h to m/s
To work with the time in seconds, we need to convert the speeds of the trains from kilometers per hour to meters per second. The conversion factor is:
\[ 1 \text{ km/h} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{1}{3.6} \text{ m/s} \]

So, we convert the speeds:
- Speed of the first train, \( v_1 = 36 \text{ km/h} = \frac{36}{3.6} = 10 \text{ m/s} \)
- Speed of the second train, \( v_2 = 54 \text{ km/h} = \frac{54}{3.6} = 15 \text{ m/s} \)

### Step 2: Calculate the relative speed
Since the trains are moving in opposite directions, we add their speeds to find the relative speed:
\[ v_{relative} = v_1 + v_2 = 10 \text{ m/s} + 15 \text{ m/s} = 25 \text{ m/s} \]

### Step 3: Use the relative speed to find the distance covered in 2 seconds
The distance covered when they cross each other can be calculated using the formula:
\[ \text{Distance} = \text{Relative Speed} \times \text{Time} \]
Given that the time taken to cross each other is 2 seconds:
\[ \text{Distance} = 25 \text{ m/s} \times 2 \text{ s} = 50 \text{ m} \]

### Step 4: Determine the length of the second train
When two trains cross each other, the total distance covered is the sum of the lengths of both trains. Let \( L_1 \) be the length of the first train and \( L_2 \) be the length of the second train. The equation can be expressed as:
\[ L_1 + L_2 = 50 \text{ m} \]

However, we need to find the length of the second train \( L_2 \). To do this, we need to know the length of the first train. Since the problem does not provide \( L_1 \), we can assume it is negligible or we can denote it as \( L_1 \).

### Step 5: Final Calculation
If we assume the length of the first train is negligible compared to the total distance, then:
\[ L_2 \approx 50 \text{ m} \]

To convert this length into kilometers:
\[ L_2 = \frac{50 \text{ m}}{1000} = 0.05 \text{ km} \]

### Final Answer
The length of the second train is approximately **0.05 km**.

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