Question

give the expression to find relative velocity

Answer 1

Suppose we have two bodies A and B moving with velocities v a and v b respectively. 

Then the relative velocity of A w.r.t B is given by, v a,b = v a - v b  

And the relative velocity of B w.r.t A is given by, v b,a = v b – v a  

Thus relative velocity of a moving body, A, with respect to another moving body, B, is found by considering B to be fixed and then finding the velocity of A which an observer resting on B will observe. 

 

When A and B are moving the the same direction and their respective velocities are v aand v b . Then, the relative velocity of A w.r.t B is given by, v a,b = v a - v b  

And the relative velocity of B w.r.t A is given by, v b,a = v b – v a  

 

When A and B are moving towards each other. The velocity of A will be v a and the velocity of B will be –v b . The negative sign appears because the direction of velocities are opposite. 

So, relative velocity of A w.r.t B is, v a,b = v a – (-v b ) = v a + v b  

And the relative velocity of B w.r.t. A is, v b,a = -v b - v a = -(v a + v b ) 

Answer 2

Answer:

The relative velocities are the time derivatives of the position vectors. Therefore, →vPS=→vPS′+→vS′S. The velocity of a particle relative to S is equal to its velocity relative to S′ plus the velocity of S′ relative to S

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