Two trains, each `50 m` long, are travelling in opposite directions with velocities `10 ms^-1 and 15 ms^-1`. The time of their crossing each other is.

Options

A. 2 s
B. 4 s
C. `2 sqrt(3)`
D. `4 sqrt(3)`

Explanation

To solve the problem of the two trains crossing each other, we can follow these steps:

### Step 1: Understand the Problem
We have two trains, each 50 meters long, moving in opposite directions with velocities of 10 m/s and 15 m/s. We need to determine the time it takes for them to completely cross each other.

### Step 2: Calculate the Total Distance to be Covered
When two objects are moving towards each other, the total distance they need to cover to completely pass each other is the sum of their lengths.

- Length of Train 1 = 50 m
- Length of Train 2 = 50 m
- Total Distance = Length of Train 1 + Length of Train 2 = 50 m + 50 m = 100 m

### Step 3: Calculate the Relative Velocity
Since the trains are moving in opposite directions, we can add their velocities to find the relative velocity.

- Velocity of Train 1 (V1) = 10 m/s (in one direction)
- Velocity of Train 2 (V2) = 15 m/s (in the opposite direction)

The relative velocity (V_rel) is given by:
\[ V_{rel} = V_1 + V_2 = 10 \, \text{m/s} + 15 \, \text{m/s} = 25 \, \text{m/s} \]

### Step 4: Calculate the Time to Cross Each Other
Now, we can use the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Velocity}} \]

Substituting the values we have:
\[ \text{Time} = \frac{100 \, \text{m}}{25 \, \text{m/s}} = 4 \, \text{s} \]

### Conclusion
The time taken for the two trains to completely cross each other is **4 seconds**.

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