A train of 150 m length is going towards North at a speed of 10 m/s. A bird is flying at 5 m/s parallel to the track towards South. The time taken by the bird to corss the train is

Options

A. 10 s
B. 15 s
C. 30 s
D. 12 s.

Answer

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

### Step 1: Understand the problem
We have a train that is 150 meters long moving north at a speed of 10 m/s, and a bird flying south at a speed of 5 m/s. We need to find out how long it takes for the bird to cross the entire length of the train.

### Step 2: Determine the relative speed
Since the bird and the train are moving in opposite directions, we can calculate the relative speed of the bird with respect to the train.

- Speed of the bird = 5 m/s (south)
- Speed of the train = 10 m/s (north)

The relative speed (V_relative) is the sum of their speeds because they are moving towards each other:

\[ V_{\text{relative}} = V_{\text{bird}} + V_{\text{train}} \]

Substituting the values:

\[ V_{\text{relative}} = 5 \, \text{m/s} + 10 \, \text{m/s} = 15 \, \text{m/s} \]

### Step 3: Calculate the time taken to cross the train
Now, we need to find the time taken (t) for the bird to cross the train. The distance to be covered is the length of the train, which is 150 meters.

Using the formula for time:

\[ t = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values:

\[ t = \frac{150 \, \text{m}}{15 \, \text{m/s}} \]

Calculating the time:

\[ t = 10 \, \text{seconds} \]

### Final Answer
The time taken by the bird to cross the train is **10 seconds**.

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