A goods train 100 m long is moving towards north with a velocity of `10_(ms^(-1))` Abird also flies due north with a velocity 15 parallel to the train. The time taken by the bird to overtaken the train is

Options

A. `10s
B. 20s
C. 4s
D. 40s

Explanation

To solve the problem of how long it takes for the bird to overtake the train, we can follow these steps:

### Step 1: Identify the given data
- Length of the train (L) = 100 m
- Velocity of the train (V_train) = 10 m/s (towards north)
- Velocity of the bird (V_bird) = 15 m/s (also towards north)

### Step 2: Calculate the relative velocity of the bird with respect to the train
To find the time taken by the bird to overtake the train, we need to determine the relative velocity of the bird with respect to the train.

\[ V_{relative} = V_{bird} - V_{train} \]
\[ V_{relative} = 15 \, m/s - 10 \, m/s = 5 \, m/s \]

### Step 3: Use the formula for time
The time taken (t) for the bird to overtake the train can be calculated using the formula:

\[ t = \frac{S}{V_{relative}} \]

Where:
- S = distance to be covered (length of the train) = 100 m
- \( V_{relative} \) = 5 m/s (calculated in the previous step)

### Step 4: Substitute the values into the formula
\[ t = \frac{100 \, m}{5 \, m/s} = 20 \, s \]

### Conclusion
The time taken by the bird to overtake the train is **20 seconds**.

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