E1.3 Kinematics (Relative Velocity):

The velocity of one body with respect to another body is called relative velocity.

Determination the Relative Velocity as follows:

I) When two objects are moving in the same direction:
When two bodies $A$ and $B$ are moving in the same direction with velocity $V_A$ and $V_B$ respectively. Then relative velocity of $A$ with respect to $B$ is:

$V_{AB} = V_A - V_B$ 

Also, the relative velocity of $B$ with respect to $A$ is:

$V_{BA} = V_B - V_A$ 

 

II) When two objects are moving in the opposite direction: 

When two bodies $A$ and $B$ are moving in the opposite direction with velocity $V_A$ and $V_B$ respectively. Then relative velocity of $A$ with respect to $B$ is:

$V_{AB}$ = $V_A - (-V_B)$ = $V_A + V_B$

 

III) When two bodies are moving inclined to each other: 

When two bodies $A$ and $B$ are moving with velocities $V_A$ and $V_B$ in different directions making an angle $\theta$. 

To find the velocity of B with respect to A, taking a velocity of A is reversed then taking $V_B$ and $-V_A$ as two sides of a parallelogram. The resultant gives the relative velocity as shown in figure.

(Similarly for relative velocity of A with respect to B).

Example: Rain falling vertically downward
                 Relative Velocity - ppt Slide

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