A train 50m long passes over a bridge at a velocity of 30 km/m. If it takes 36 s to cross the bridge, the length of the bridge will be

Options

A. 100 m
B. 200m
C. 250m
D. 300m

Explanation

To find the length of the bridge, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed of the train is given as 30 km/h. To convert this to meters per second (m/s), we use the conversion factor:
1 km/h = (1000 m / 3600 s).

So, we calculate:
\[ \text{Speed in m/s} = 30 \times \frac{1000}{3600} = \frac{30000}{3600} \approx 8.33 \text{ m/s} \]

### Step 2: Calculate the total distance traveled by the train while crossing the bridge
The train takes 36 seconds to cross the bridge. The total distance traveled by the train in this time can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values we have:
\[ \text{Distance} = 8.33 \text{ m/s} \times 36 \text{ s} \approx 299.88 \text{ m} \]

### Step 3: Calculate the length of the bridge
The total distance traveled by the train while crossing the bridge includes the length of the train and the length of the bridge. We know the length of the train is 50 m. Therefore, we can set up the equation:
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Bridge} \]
Let \( L \) be the length of the bridge. Then:
\[ 299.88 = 50 + L \]

### Step 4: Solve for the length of the bridge
Rearranging the equation gives:
\[ L = 299.88 - 50 = 249.88 \text{ m} \]

Thus, the length of the bridge is approximately 249.88 m.

### Final Answer
The length of the bridge is approximately **249.88 meters**.

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