A passenger sitting by the window of a train moving with a velocity of 72 km/h observes for 10 seconds that a train moving with a velocity of `32.4` km/h completely passes by it in 10 seconds. The lengthof the second train is

Options

A. 110m
B. 145m
C. 210m
D. 290m

Answer

To find the length of the second train as observed by a passenger in the first train, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the velocities from km/h to m/s**:
- The velocity of the first train (observer's train) is given as 72 km/h.
- The velocity of the second train is given as 32.4 km/h.
- To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \).
- Therefore:
\[ v_A = 72 \times \frac{5}{18} = 20 \, \text{m/s} \]
\[ v_B = 32.4 \times \frac{5}{18} = 9 \, \text{m/s} \]

2. **Determine the relative velocity of the second train with respect to the first train**:
- Since the second train is moving in the opposite direction to the observer, the relative velocity \( v_{BA} \) is given by:
\[ v_{BA} = v_B + v_A = 9 + 20 = 29 \, \text{m/s} \]

3. **Calculate the length of the second train**:
- The second train completely passes the observer in 10 seconds. The length of the train can be calculated using the formula:
\[ \text{Length} = \text{Relative Velocity} \times \text{Time} \]
- Substituting the values:
\[ \text{Length} = 29 \, \text{m/s} \times 10 \, \text{s} = 290 \, \text{m} \]

### Final Answer:
The length of the second train is **290 meters**.

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