Have you ever notice when you are traveling on a bus and
observe out from the window of the bus, objects on the ground are moving? OR
when you are running, have you ever feel suddenly, the wind is starting to flow
around you and when you stop, the wind also stops to flow? Similarly, when two
vehicles cross each other in the opposite direction, the velocity of one
vehicle observed by another person on another vehicle is more than the velocity
of that vehicle observed by a person at rest on the ground. All those examples
indicate that the velocity of one object depends on the velocity of the body
from which it is observed. In all those process phenomena of relative velocity
works. The relative velocity refers to the velocity of one body concerning
another body.
Mathematical description of relative velocity
The relative velocity represents the resultant of vector subtraction. It can be obtained by calculating the resultant of vector addition between and which gives the vector subtraction . So, the relative velocity of body A with respect to body B with velocity and respectively is given by
The magnitude of is given by
Now, consider different conditions
Condition 1: When two bodies A and B are moving in the same direction
Let suppose body A is moving with velocity and body B is moving with velocity in same direction the relative velocity of A with respect to B is given by
The magnitude of is given by
Condition 2: When two bodies A and B are moving in opposite direction
Let us suppose body A is moving with velocity velocity and body B is moving with velocity in the opposite direction. Now the relative velocity of body A with respect to body B is given by
The magnitude of is given by
Condition 3: When two body making an acute angle θ (90˚>θ>0˚)
Let us suppose body A is moving with velocity and body B is moving with velocity making angle θ between them. Now the relative velocity of body A with respect to body B is given by
The magnitude of is given by
The value of cosθ when the value of θ is between 90˚ and 0˚ ranges from 0 to 1 which is a positive value.
From above three condition we can say that
Now let’s looks out some real life examples of relative velocity
a) When a person looks out from the window on moving bus
Assume that a person setting on a bus moving with some velocity and he look at a tree out from the bus window the tree is at rest so its velocity the relative velocity of tree with respect to the person on the bus is given by
The magnitude of is given by
So this implies that the magnitude of relative velocity is equal to the velocity of bus and opposite in direction
b) When two vehicles cross each other
Let suppose that two vehicles are moving with velocities and respectively in opposite directions to each other. The relative velocity of bus A with respect to bus B is given by
The magnitude of is given by
The magnitude of is given by
It concludes that the relative velocity of bus A with respect to bus B is greater than the velocity of bus A observed by a person on ground because velocity will be on ground.
c) When a person walking on rain
When a person walks in the rain with an umbrella in his hand. He needs his umbrella to hold a little bit of incline that is due the relative velocity of rain. Let a person walking with velocity on rain and the rain is dropping vertically with the velocity of then the relative velocity of rain with respect to the person walking on rain is given by
The magnitude of is given by
The below picture shows the relative velocity used in real life
