In what time will a train 100 metres long with a speed of 50 km/hour cross a pillar?

Options

A. 7 seconds
B. 72 seconds
C. 7.2 seconds
D. 70 seconds

Answer

To solve the problem of how long it will take for a train that is 100 meters long to cross a pillar at a speed of 50 km/hour, we can follow these steps:

### Step 1: Understand the Problem
We need to determine the time it takes for the entire length of the train (100 meters) to pass a stationary object (the pillar).

### Step 2: Identify the Given Information
- Length of the train = 100 meters
- Speed of the train = 50 km/hour

### Step 3: Convert Speed to Meters per Second
Since the distance is given in meters, we need to convert the speed from kilometers per hour to meters per second.

To convert km/hour to m/s, we use the conversion factor:
1 km/hour = (1000 meters / 3600 seconds) = 1/3.6 m/s

Thus, to convert 50 km/hour to m/s:
\[ \text{Speed in m/s} = 50 \times \frac{1000}{3600} = \frac{50000}{3600} \approx 13.89 \text{ m/s} \]

### Step 4: Use the Formula for Time
The formula for time when distance and speed are known is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance is the length of the train (100 meters) and the speed is now in meters per second (approximately 13.89 m/s).

### Step 5: Calculate the Time
Substituting the values into the formula:
\[ \text{Time} = \frac{100 \text{ meters}}{13.89 \text{ m/s}} \approx 7.2 \text{ seconds} \]

### Final Answer
The time taken for the train to cross the pillar is approximately **7.2 seconds**.

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