# Relative Velocity – Learn with Examples & FAQs

We are sharing this article on Relative Velocity to help you in your preparation for competitive exams for Engineering such as BITSAT and JEE Main. Here in this article, our experts have explained in detail what is the relative velocity with examples and illustrations, and related FAQs for strengthening your preparations to crack the exam you are appearing for!

**What is Relative Velocity?**

Consider any two bodies which are moving relative to each other. **Relative velocity** is the velocity that the first body would appear to an observer on the second body. Similarly, the velocity that the second body would appear to an observer on the first body.

In mathematics, the **relative velocity** is the vector difference of the velocities between the two bodies.

**Relative velocity**= Velocity of the first body – Velocity of the second body

Or

V12 = V1 – V2

**Relative velocity **is used to describe the motion of airplanes in the wind etc. This velocity is calculated according to the observer present in the object. Different frames of reference are used in this type of velocity.

When we are traveling in a bus, car, or train, we see many things like trees, buildings, etc outside going backward. But they are not really going backward. It’s our vehicle that is moving but the trees are stationary. Here the **relative velocity** is the velocity difference between us and the trees.

**Examples of Relative Velocity**

**Some Illustrations Regarding the Relative Velocity:**

**Illustration I: **

A plane is traveling at a velocity of 100 km/hr, in the southward direction. It encounters wind traveling in the west direction at a rate of 25 km/hr. Calculate the resultant velocity of the plane.

**Solution: **

Given, the velocity of the wind = Vw = 25km/hr

The velocity of the plane = Va= 100 km/hr

The relative velocity of the plane with respect to the ground can be given as

The angle between the velocity of the wind and that of the plane is 90°. Using the Pythagorean theorem, the resultant velocity can be calculated as,

R2= (100 km/hr)2 + (25 km/hr)2

R2= 10 000 km2/hr2 + 625 km2/hr2

R2= 10 625 km2/hr2

Hence, **R = 103.077 km/hr**

**Illustration II:**

A motorcycle traveling on the highway at a velocity of 120 km/h passes a car traveling at a velocity of 90 km/h. From the point of view of a passenger in the car, what is the velocity of the motorcycle?

**Solution: **

Let us represent the velocity of the motorcycle as *VA *and the velocity of the car as *VB*.

Now, the velocity of the motorcycle relative to the point of view of a passenger is given as

*VAB* = *VA* – *VB*

Substituting the values in the above equation, we get

*VAB *= 120 km/h – 90 km/h = 30 km/h

Hence, the velocity of the motorcycle relative to the passenger of the car is 30 km/h.

**Illustration III:**

An airplane flies with a velocity of 450 m/s to the north, while an airplane B travels at a velocity of 500 m/s to the south beside airplane A. Calculate the relative velocity of airplane A with respect to B.

**Solution:**

The relative velocity of airplane A with respect to the velocity of airplane B is calculated as follows:

*VAB* = *VA* – *VB*

Substituting the values in the equation, we get

*VAB* = 350 m/s – (–500 m/s) = 850 m/s

The velocity of airplane B is considered negative, as it flies in the opposite direction to airplane A.

So, this is all about the Relative Velocity. Get some practice of the same on our free Testbook App. Download Now!

**Frequently Asked Questions Related to Relative Velocity**

**Q.1 Can relative speed be negative?**

**Ans.1**

Yes, it can be negative as it is the difference of two velocities irrespective of which velocity is more in magnitude.

**Q.2 What is the difference between velocity and relative velocity?**

**Ans.2**

The velocity is measured with respect to a reference point that is relative to something else whereas relative velocity is measured in a frame that is itself at rest or moving with respect to the absolute frame.

**Q.3 Why is there a need of using relative velocity?**

**Ans.3**

There is a need of using this term to clear the misconception of objects being stationary or moving.