Relative Velocity Formula

When we are traveling in a car or bus then we can see the trees and buildings outside, going backward. But are they really going backward? No, as we know that it is our vehicle that is moving while the trees are stationary on the ground. So, then why do the trees appear to be moving backward? On the other hand, the co-passengers with us who are moving, but appear stationary to us despite moving. This concept is explained in physics with the help of relative velocity. In this topic, we will see the relative velocity formula withy examples. Let us learn it!

Source:en.wikipedia.org 

Relative Velocity Formula

What is relative velocity?

Since we and our co-passengers are moving together. Therefore, there is no relative velocity between us and the passengers. Also, the trees are stationary while we moving. Thus, the trees are moving at some relative velocity with respect to us and the other passengers. Here, the relative velocity is the difference of velocities between you and the tree.

Relative velocity is generally used to describe the motion of airplanes in the wind or moving boats through water etc. This velocity is computed according to the person as an observer inside the object. This can be determined by introducing an intermediate frame of reference.

Let us consider two objects A and B which are moving relative to each other. Then the relative velocity will be the velocity in which a body A would appear to body B and vice versa. Mathematically, we nay say that the relative velocity will be the vector difference between the velocities of two objects.

The relative velocity of A with respect to B= velocity of the body A – velocity of the body B.

Mathematically,

V_{AB} = V_{A}– V_{B}

Where:

V_{AB}  relative velocity of the body A respect body B

V_{A}  velocity of the body A

V_{B} velocity of body B

Solved examples:

Q.1: An aircraft A flies to the north with a velocity of 350 m s^{-1}. Another aircraft B flies to the south with the velocity of 500 m s^{-1} beside aircraft A. Calculate the following:

1. The relative velocity to the aircraft A respect aircraft B.
2. The relative velocity to the aircraft A respect aircraft B, but now both fly to the north.
3. Compare both the results.

Solution: Given parameters are:

V_{A} = 350 m s^{-1}.

V_{B} = 500 m s^{-1}

1. Then using the formula for relative velocity,

V_{AB} = V_{A}– V_{B}

= 350 – (-500 )

= 850 m s^ {-1}

The relative velocity to the aircraft A respect aircraft B will be 850 m s^ {-1}. Here, we have considered the velocity of the aircraft B as negative because it flies towards the opposite direction to the aircraft A.

2. Now, using the formula for relative velocity,

V_{AB} =  V_{A}– V_{B}

= 350  – 500

= 150 m s^ {-1}

Thus, the relative velocity to the aircraft A respect aircraft B will be 150 m s^ {-1}. Here, we have considered the velocity of the aircraft B as positive because it flies in the same direction of the aircraft A.

3. For a person as an observer on the aircraft A in the first case, the relative velocity with respect to the aircraft B is higher compared to the second case. This is because, they are moving away very fast, while in the second case they are approaching.