A passenger sitting in a train A moving at `90` km/h observes another train B moving inthe opposite direction for `8 s` .If the velocity of the train B is `54` km/h,then lengh of train B is :

Options

A. `120 m`
B. `320 m`
C. `200 m`
D. `80 m`

Answer

To solve the problem, we need to determine the length of train B based on the information provided. Here’s a step-by-step solution:

### Step 1: Understand the relative motion
The two trains are moving in opposite directions. Therefore, to find the relative speed, we need to add the speeds of both trains.

### Step 2: Convert speeds from km/h to m/s
- Speed of train A = 90 km/h
- Speed of train B = 54 km/h

To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \).

- Speed of train A in m/s:
\[ 90 \text{ km/h} = 90 \times \frac{5}{18} = 25 \text{ m/s} \]

- Speed of train B in m/s:
\[ 54 \text{ km/h} = 54 \times \frac{5}{18} = 15 \text{ m/s} \]

### Step 3: Calculate the relative speed
Now, we add the speeds of both trains to find the relative speed:
\[ \text{Relative speed} = 25 \text{ m/s} + 15 \text{ m/s} = 40 \text{ m/s} \]

### Step 4: Calculate the distance observed
The passenger observes train B for 8 seconds. The distance covered by train B during this time can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values we have:
\[ \text{Distance} = 40 \text{ m/s} \times 8 \text{ s} = 320 \text{ m} \]

### Step 5: Conclusion
The length of train B is therefore 320 meters.

### Final Answer:
The length of train B is **320 meters**.

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