A 175 m long train is travelling along a straight track what a velocity `72 km h^(-1)`. A bird is flying parallel to the train in the opposite direction with a velocity `18 kmh^(-1)`. The time taken by the bird to cross the train is

Options

A. 35 s
B. 27 s
C. 11.6 s
D. 7 s

Explanation

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

### Step 1: Write down the given data
- Length of the train (L) = 175 m
- Velocity of the train (V_train) = 72 km/h
- Velocity of the bird (V_bird) = 18 km/h

### Step 2: Convert velocities from km/h to m/s
To convert km/h to m/s, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{1}{3.6} \text{ m/s} \]

- Velocity of the train in m/s:
\[ V_{train} = 72 \text{ km/h} \times \frac{1}{3.6} = 20 \text{ m/s} \]

- Velocity of the bird in m/s:
\[ V_{bird} = 18 \text{ km/h} \times \frac{1}{3.6} = 5 \text{ m/s} \]

### Step 3: 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 add their speeds to find the relative velocity:
\[ V_{relative} = V_{train} + V_{bird} = 20 \text{ m/s} + 5 \text{ m/s} = 25 \text{ m/s} \]

### Step 4: Calculate the time taken by the bird to cross the train
The time taken (T) to cross the train can be calculated using the formula:
\[ T = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance is the length of the train (175 m) and the speed is the relative speed (25 m/s):
\[ T = \frac{175 \text{ m}}{25 \text{ m/s}} = 7 \text{ seconds} \]

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

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