Question

A car A moves with velocity $15m{s}^{-1}$ and B with velocity $20m{s}^{-1}$ are moving in opposite directions as shown in the figure. Find the relative velocity of B w.r.t. A and A w.r.t. B.

Answer 1

Here also let us assume the right direction is positive, then the left direction will be negative.
Given: $v_A=-15ms-1$, $v_B=20ms-1$
Relative velocity of B w.r.t A:
$v_{B_{/}A}=v_B-v_A=20-(-15)=35m{s}^{-1}$ (Positive sign indicates that this relative velocity is in right direction.)
Relative velocity of A w.r.t B: $v_{A_{/}B}=v_A-v_B=-15-20=-35m{s}^{-1}$ (Negative sign indicates that this relative velocity is in backward direction.)
Here the separation between A and B is increasing with time, hence the velocity of separation is $35m{s}^{-1}$.