A pigeon flies at 36 km/h to and for between two cars moving toward each other on a straight road, starting from the first car when the car separation is 40 km. The first car has speed of 16 km/h and the second one has a speed of 25 km/h. By the time the cars meet head on, what are the (a) total distance and (b) net displacement flown by the pigeon ?

Answer

To solve the problem, we need to determine the total distance and net displacement flown by the pigeon while the two cars are moving towards each other.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Speed of the first car (Car A) = 16 km/h
- Speed of the second car (Car B) = 25 km/h
- Speed of the pigeon = 36 km/h
- Initial separation between the cars = 40 km

2. **Calculate the Relative Speed of the Cars:**
Since the two cars are moving towards each other, their relative speed is the sum of their speeds:
\[ \text{Relative Speed} = \text{Speed of Car A} + \text{Speed of Car B} = 16 \text{ km/h} + 25 \text{ km/h} = 41 \text{ km/h} \]

3. **Calculate the Time Taken for the Cars to Meet:**
The time taken for the cars to meet can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{40 \text{ km}}{41 \text{ km/h}} \approx 0.9756 \text{ hours} \]

4. **Calculate the Distance Flown by the Pigeon:**
The distance flown by the pigeon can be calculated using the formula:
\[ \text{Distance} = \text{Speed of Pigeon} \times \text{Time} \]
Substituting the values:
\[ \text{Distance} = 36 \text{ km/h} \times 0.9756 \text{ hours} \approx 35.1 \text{ km} \]

5. **Determine the Net Displacement of the Pigeon:**
The net displacement of the pigeon is the distance between the two cars when they meet. Since the pigeon flies back and forth between the two cars, its net displacement will be equal to the initial distance between the two cars, which is 40 km.

### Final Answers:
(a) Total distance flown by the pigeon = 35.1 km
(b) Net displacement flown by the pigeon = 40 km