Two trains are approaching each other on the same track with velocity 100 km/h and 50 km/h. When they are at a distance of 300 km from each other, a bird starts flying from train 1 towards train 2. When the bird reaches train 2, it instantly reverses its direction and flies again towards train 1. This process continues till the bird is trapped between the trains when they collide. If the bird always travels at a constant speed 200 km/h, the total distance the bird flies is:

Options

A. 200 km
B. 400 km
C. 300 km
D. 600 km

Explanation

To solve the problem, we need to determine the total distance that the bird flies before the two trains collide. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the velocities of the trains
The velocities of the two trains are given as:
- Train 1 (V1) = 100 km/h
- Train 2 (V2) = 50 km/h

### Step 2: Calculate the relative velocity of the trains
Since the trains are moving towards each other, their relative velocity (V12) can be calculated by adding their speeds:
\[ V_{12} = V_1 + V_2 = 100 \text{ km/h} + 50 \text{ km/h} = 150 \text{ km/h} \]

### Step 3: Calculate the time until the trains collide
The initial distance between the two trains is 300 km. We can find the time (t) taken for the trains to collide using the formula:
\[ t = \frac{\text{Distance}}{\text{Relative Velocity}} \]
Substituting the values:
\[ t = \frac{300 \text{ km}}{150 \text{ km/h}} = 2 \text{ hours} \]

### Step 4: Determine the speed of the bird
The speed of the bird is given as:
- Speed of the bird (V_bird) = 200 km/h

### Step 5: Calculate the total distance flown by the bird
The total distance (D_bird) that the bird flies can be calculated using the formula:
\[ D_{bird} = \text{Speed of the bird} \times \text{Time until collision} \]
Substituting the values:
\[ D_{bird} = 200 \text{ km/h} \times 2 \text{ hours} = 400 \text{ km} \]

### Conclusion
The total distance that the bird flies before it gets trapped between the two trains is **400 km**.

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