Relative Velocity

Relative velocity is the velocity in 2 different frames. You might have experienced trees moving back while we are inside a moving vehicle. In reality, they are not, instead they are stationary and we are moving. You get a perception that they are moving becasue we are in a different frame. Therefore, trees and the vehicle are in 2 different frames making you feel like you are moving. Let us say Frame-A is where you are sitting in the moving car and the frame B is the stationary trees. Now since 2 frames are in a different state (one is moving another is stationary), you experience a relative change in the velocity.  “The relative velocity is the velocity that the body-A would appear to the body-B(an observer) and vice versa”. When we put it in a mathematical way, it is the vector difference between the velocities of two different bodies. In simple terms, the velocity of an object with respect to another object is called the relative velocity. If there are two moving objects A and B, the velocity of A with respect to B is the velocity that A would appear to have when observed from B.  Consider an object A moving with a velocity, VA and an object B moving with a velocity, VB in the same direction. The velocity of object A with respect to B or the relative velocity of object A is,

Relative velocity = velocity of the body A – velocity of the body B,

I, e vAB = vA – vB

vAB: relative velocity of the body A respect body B

vA: velocity of the body A

vB: velocity of the body B

Question: The river flows with a velocity 10 m/s. A man swims parallel to the river bank in the same direction as the flow of the river with a velocity of 2 m/s.

1. What is the relative velocity of the man?

2. What is the relative velocity of the man if he is moving against the flow of the river?

Answer:

  1. 8 m/s

  2. 12 m/s

 



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