A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has a speed of `18 km //h` while the other has the speed of ` 27 km //h`. The bird starts moving from first car towards the other and is moving with the speed of ` 36 km //h` and when the two cars were separated by ` 36 km`. What is the total distance covered by the bird ? What is the total displacement of the bird ?

Options

A. 28.8 km
B. 38.8 km
C. 48.8 km
D. 58.8 km

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the speeds of the cars and the bird
- Speed of the first car (Car A) = 18 km/h
- Speed of the second car (Car B) = 27 km/h
- Speed of the bird = 36 km/h

### Step 2: Calculate the relative speed of the two cars
The relative speed of the two cars moving towards each other is the sum of their speeds:
\[ \text{Relative Speed} = \text{Speed of Car A} + \text{Speed of Car B} \]
\[ \text{Relative Speed} = 18 \text{ km/h} + 27 \text{ km/h} = 45 \text{ km/h} \]

### Step 3: Determine the initial distance between the two cars
The initial distance between the two cars is given as:
\[ \text{Distance} = 36 \text{ km} \]

### Step 4: Calculate the time taken for the cars to meet
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]
\[ \text{Time} = \frac{36 \text{ km}}{45 \text{ km/h}} = 0.8 \text{ hours} \]

### Step 5: Calculate the distance traveled by the bird
The distance traveled by the bird can be calculated using the formula:
\[ \text{Distance} = \text{Speed of the bird} \times \text{Time} \]
\[ \text{Distance} = 36 \text{ km/h} \times 0.8 \text{ hours} = 28.8 \text{ km} \]

### Step 6: Determine the total displacement of the bird
Since the bird starts from the first car and flies towards the second car, its displacement is equal to the distance between the two cars when they meet. Therefore:
- Total displacement = Distance between the two cars = 36 km

### Final Answers:
- Total distance covered by the bird = 28.8 km
- Total displacement of the bird = 36 km

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