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: Identify the speeds and directions
- The train is moving due north at a speed of 25 m/s.
- The bird is flying due south at a speed of 5 m/s.

### Step 2: Determine the relative velocity of the bird with respect to the train
- Since the bird is flying in the opposite direction to the train, we need to add their speeds to find the relative velocity.
- Relative velocity of the bird with respect to the train = Speed of the bird + Speed of the train
\[ \text{Relative velocity} = 5 \, \text{m/s} + 25 \, \text{m/s} = 30 \, \text{m/s} \]

### Step 3: Calculate the time taken to cross the train
- The length of the train is 210 meters.
- The time taken to cross the train can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Velocity}} \]
- Substituting the values:
\[ \text{Time} = \frac{210 \, \text{meters}}{30 \, \text{m/s}} = 7 \, \text{seconds} \]

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

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