Two trains are each 50 m long moving parallel towards each other at speeds `10 ms^(-1)` and `15 ms^(-1)` respectively, at what time will they pass each other ?

Options

A. 8 s
B. 4 s
C. 2 s
D. 6 s

Explanation

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

### Step 1: Understand the problem
We have two trains, each 50 meters long, moving towards each other. Train A is moving at a speed of 10 m/s, and Train B is moving at a speed of 15 m/s.

### Step 2: Calculate the relative velocity
When two objects are moving towards each other, their relative velocity is the sum of their speeds.

- Velocity of Train A (VA) = 10 m/s (towards the right)
- Velocity of Train B (VB) = 15 m/s (towards the left)

The relative velocity (V_AB) of Train A with respect to Train B is:
\[ V_{AB} = V_A + V_B = 10 \, \text{m/s} + 15 \, \text{m/s} = 25 \, \text{m/s} \]

### Step 3: Calculate the total distance to be covered
Since both trains are 50 meters long, the total distance (D) that needs to be covered for them to completely pass each other is the sum of their lengths:
\[ D = \text{Length of Train A} + \text{Length of Train B} = 50 \, \text{m} + 50 \, \text{m} = 100 \, \text{m} \]

### Step 4: Calculate the time taken to pass each other
Using the formula for time, which is distance divided by velocity:
\[ \text{Time} (t) = \frac{D}{V_{AB}} \]
Substituting the values we have:
\[ t = \frac{100 \, \text{m}}{25 \, \text{m/s}} = 4 \, \text{s} \]

### Final Answer
The time taken for the two trains to pass each other is **4 seconds**.

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