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

### Step 1: Understand the velocities
The first train is moving at a velocity of 72 km/h, and the second train is moving at a velocity of 32.4 km/h.

### Step 2: Convert velocities to the same unit
To make calculations easier, we will convert these velocities from km/h to m/s using the conversion factor \( \frac{5}{18} \):
- Velocity of the first train:
\[ 72 \text{ km/h} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]
- Velocity of the second train:
\[ 32.4 \text{ km/h} = 32.4 \times \frac{5}{18} = 9 \text{ m/s} \]

### Step 3: Calculate the relative velocity
Since both trains are moving towards each other, we add their speeds to find the relative velocity:
\[ \text{Relative Velocity} = 20 \text{ m/s} + 9 \text{ m/s} = 29 \text{ m/s} \]

### Step 4: Use the time to find the length of the second train
The second train completely passes the observer in 10 seconds. We can use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Here, the distance is the length of the second train (L), speed is the relative speed (29 m/s), and time is 10 seconds:
\[ L = 29 \text{ m/s} \times 10 \text{ s} = 290 \text{ meters} \]

### Conclusion
The length of the second train is **290 meters**.

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