Question

A bird flies with a speed of $ 10\dfrac{{km}}{{hr.}} $ and a car moves with a uniform speed of $ 8\dfrac{{km}}{{hr.}} $ . Both start from $ B $ towards $ A $ ( $ BA = 40km $ ) at the same instant. The bird having reached $ A $ , flies back immediately to meet the approaching car. As soon as it reaches the car, it flies back to $ A $ . The bird repeats this till both the car and the bird reach $ A $ simultaneously. Find the total distance flown by the bird.

Answer 1

Hint: Speed is a scalar (independent of direction) quantity and velocity is a vector (dependent on direction) quantity. Distance is a scalar quantity and displacement is a vector quantity. On changing the direction of motion, distance travelled by the body always increases but the displacement of the body may increase or decrease.

Formula used:

$v = \dfrac{d}{t} $

Where $ v $ speed and $ d $ is the distance and $ t $ is the time taken to cover that distance with the given speed.

Complete step by step answer

From the question, we can say that

Total distance travelled by car is $ 40km $ .

Speed of the car is $ 8\dfrac{{km}}{{hr.}} $

Speed of the bird is $ 10\dfrac{{km}}{{hr.}} $

Time taken by the car and the bird to come to reach A after the motion started will be the same. This can be figured out by reading the question.

Now we begin to the mathematics of the question,

Total time taken by car to come to rest is

 $\Rightarrow t = \dfrac{d}{v} $

Where $ v $ speed and $ d $ is the distance and $ t $ is the time taken to cover that distance with the given speed.

 $\Rightarrow t = \dfrac{{40km}}{{8kmh{r^{ - 1}}}} $

 $\Rightarrow t = 5hr $

Hence,

The total distance flown by the bird will be

 $\Rightarrow d = vt $

The bird was changing the direction of motion continuously but then also the speed of the bird remained the same as both are scalar quantities.

$\Rightarrow d = 10kmh{r^{ - 1}} \times 5hr $

$\therefore d = 50km $

Hence the correct answer to our question is $ 50km $.

Note:

There is one more method to solve this question but it will be very long hence it was not made the primary solution. In that solution, you need to keep a track of what time the direction of motion of the bird is changing whenever it changes, calculate the distance travelled by it in that interval.