Question

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

Answer 1

Hint: Here, we use the term speed; the speed is the rate of change of the distance. The expression be used
$speed = \dfrac{{distance}}{{time}}$

Complete answer:
According to the question, the given condition is,
Distance between the cars = 40 km,
Speed of the first car = 16km/hr,
Speed of the second car = 25km/hr
The relative speed of the car = Speed of the first car + Speed of the second car
Relative Speed of the car = (16km/hr) + (25km/hr)
Relative Speed of the car = (41km/hr)
Speed of the bird is 36 km/hr
Now, we use the above expression
$speed = \dfrac{{dis\tan ce}}{{time}}$
To find the time
$total\;time = \dfrac{{dis\tan ce}}{{relative\;speed}} \\$
$T = \dfrac{{40(km)}}{{41(km/hr)}} \\$
$T = \dfrac{{40}}{{41}}hr \\ $
(a)
The total distance travelled by the pigeon is
So, the above expression
$speed = \dfrac{{dis\tan ce}}{{time}}$
We have to calculate the total distance, so
$total\;dis\tan ce = speed\;{\text{of the bird}} \times time \\$
$total\;dis\tan ce = 36 \times \dfrac{{40}}{{41}} \\$
$total\;dis\tan ce = \dfrac{{1440}}{{41}} \\$
$total\;dis\tan ce = 35.1219km \\ $
So, the total distance is 35.1219km
(b)
The net displacement flown by the pigeon,
\[
  Distance{\text{ }}travelled{\text{ }}by{\text{ }}the{\text{ }}first{\text{ }}car{\text{ }}in{\text{ }}this{\text{ }}time{\text{ }}period{\text{ }} = {\text{ }}speed{\text{ }}of{\text{ }}first{\text{ }}car\; \times time \\
  net\;displacement\;{\text{ = }}\;{\text{16}} \times \dfrac{{40}}{{41}} \\
  net\;displacement\;{\text{ = }}\;\dfrac{{640}}{{41}} \\
  net\;displacement\;{\text{ = }}15.6097km \\ \]
So, the net displacement is 15.6097km

Note:
When we calculate the relative speed, then one thing we have to note is that the one car is assumed as a rest and the opposite velocity of the car is taken and added with the direction.
The displacement is the shortest path travelled by the body while the distance is the actual path travelled by the body.