Two trains 121 m and 99 m in length are running in opposite directions with velocities `40 km h^(-1)` and `32 km h^(-1)`. In what time they will completely cross each other?

Options

A. a. 9 s
B. b. 11 s
C. c. 13 s
D. d. 15 s

Explanation

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

### Step 1: Identify the lengths of the trains and their velocities.
- Length of Train 1 (L1) = 121 m
- Length of Train 2 (L2) = 99 m
- Velocity of Train 1 (V1) = 40 km/h
- Velocity of Train 2 (V2) = 32 km/h

### Step 2: Convert the velocities from km/h to m/s.
To convert km/h to m/s, we use the conversion factor:
\[ \text{Velocity in m/s} = \text{Velocity in km/h} \times \frac{5}{18} \]

- For Train 1:
\[ V1 = 40 \times \frac{5}{18} = \frac{200}{18} \approx 11.11 \, \text{m/s} \]

- For Train 2:
\[ V2 = 32 \times \frac{5}{18} = \frac{160}{18} \approx 8.89 \, \text{m/s} \]

### Step 3: Calculate the total distance to be covered when the trains cross each other.
The total distance (D) is the sum of the lengths of both trains:
\[ D = L1 + L2 = 121 \, \text{m} + 99 \, \text{m} = 220 \, \text{m} \]

### Step 4: Calculate the relative velocity of the two trains.
Since the trains are moving in opposite directions, we add their speeds to find the relative velocity (V_rel):
\[ V_{rel} = V1 + V2 \]
\[ V_{rel} = 11.11 \, \text{m/s} + 8.89 \, \text{m/s} = 20 \, \text{m/s} \]

### Step 5: Calculate the time taken to cross each other.
Using the formula for time (t):
\[ t = \frac{D}{V_{rel}} \]
Substituting the values we have:
\[ t = \frac{220 \, \text{m}}{20 \, \text{m/s}} = 11 \, \text{s} \]

### Final Answer:
The time taken for the two trains to completely cross each other is **11 seconds**.

---