$\require{cancel}$
I'm not even sure I should post this question here or not, but here we go.
A bird is 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 the 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?
Now, The part of finding total distance is actually easier than I thought. The relative velocity of the cars with respect to each other is $(27 + 18)$ km/h $= 45$ km/h. So, for the cars to meet, the time required:
$$\frac{\text{The distance between the cars}}{\text{Relative Velocity}} = \frac{\cancel{36}^4}{\cancel{45}^5}\text{ hours} = 0.8 \text{ hours}$$
So the distance traveled by the bird = $(36 * 0.8) \text{ km} = 28.8 \text{ km}$.
My question is, how to find the total displacement? For we all know, the bird has the highest velocity of them all, so it can get back after reaching the second car and at the time the two cars meet, it might be in motion. DIsplacement is the distance between the final and initial point of motion $(\vec{s} = \vec{r_f} – \vec{r_i}$, where $\vec{r}$ is the position vector and $\vec{s}$ is the displacement vector), so I can't figure out what to use and how.
Any help would be appreciated.
Best Answer
As you said, the time required for the cars to meet is $0.8$ hours. Where are the cars $0.8$ hours later? The first car will have travelled $14.4$ kilometers, and the second $21.6$. Thus both cars are in the same spot (duh) and since the bird stays between them, the bird is there also; hence the displacement is $14.4$ kilometers towards the second car.