A 210 meter long train is moving due north at a of 25 m/s. a small bird is flying due south a little above the train with speed 5 m/s. The time taken by the bird to cross the train is

Options

A. 6s
B. 7s
C. 9s
D. 10s

Explanation

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 210 meters long, moving due north at a speed of 25 m/s. A bird is flying due south at a speed of 5 m/s. We need to find the time taken by the bird to cross the entire length of the train.

### Step 2: Determine the relative velocity
Since the train and the bird are moving in opposite directions, we can find the relative velocity of the bird with respect to the train by adding their speeds together.

- Speed of the train (v_train) = 25 m/s (north)
- Speed of the bird (v_bird) = 5 m/s (south)

The relative velocity (v_relative) is given by:
\[ v_{\text{relative}} = v_{\text{train}} + v_{\text{bird}} \]
\[ v_{\text{relative}} = 25 \, \text{m/s} + 5 \, \text{m/s} = 30 \, \text{m/s} \]

### Step 3: Calculate the time taken to cross the train
The time taken (t) for the bird to cross the train can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Relative Velocity}} \]

Here, the distance is the length of the train, which is 210 meters.

Substituting the values:
\[ t = \frac{210 \, \text{meters}}{30 \, \text{m/s}} \]
\[ t = 7 \, \text{seconds} \]

### Final Answer
The time taken by the bird to cross the train is **7 seconds**.

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