To solve this problem, we will use the concept of relative speed and time to calculate the length of the trains. Here is the approach:

Problem Breakdown:

• Two trains of equal length are moving in the same direction.
• Speed of the faster train: $46 \ \text{km/h}$.
• Speed of the slower train: $36 \ \text{km/h}$.
• Time taken by the faster train to pass the slower train: 36 seconds.

We need to find the length of each train.

Step 1: Calculate the relative speed

Since both trains are moving in the same direction, the relative speed is the difference between their speeds: $\text{Relative speed} = 46 \ \text{km/h} - 36 \ \text{km/h} = 10 \ \text{km/h}$

Convert this speed into meters per second (m/s), since time is given in seconds: $10 \ \text{km/h} = \frac{10 \times 1000}{3600} = \frac{10000}{3600} \approx 2.78 \ \text{m/s}$

Step 2: Calculate the total distance covered

When the faster train passes the slower train, it covers a distance equal to the length of both trains combined (since the trains are of equal length). Let the length of each train be $L$ meters. Therefore, the total distance is $2L$.

Using the formula: $\text{Distance} = \text{Speed} \times \text{Time}$ The total distance covered is: $2L = 2.78 \ \text{m/s} \times 36 \ \text{seconds} = 100.08 \ \text{meters}$

Step 3: Calculate the length of one train

Since $2L = 100.08$, we divide by 2 to get the length of each train: $L = \frac{100.08}{2} \approx 50.04 \ \text{meters}$

Thus, the length of each train is approximately 50 meters.

Final Answer:

Option A (50 m) is correct.

Would you like any further explanation, or do you have any questions?

Follow-up questions:

1. What would the length be if the time to pass were 45 seconds instead of 36 seconds?
2. How would the calculation change if the trains were moving in opposite directions?
3. What is the formula for relative speed in general, and how does direction affect it?
4. How does the speed conversion from km/h to m/s work?
5. Could this problem be solved differently using graphical or diagrammatic methods?

Tip:

Always make sure to convert units (e.g., km/h to m/s) when working with speed and time in different units to avoid calculation errors.