Question

Two cars $A$ and $B$ are running at velocities of $60km{h}^{-1}$ and $45km{h}^{-1}$ . What is the relative velocity of car $A$ with respect to car $B$ , if both are moving eastward ?
What is the relative velocity of a car $A$ with respect to car $B$ , if car $A$ is moving eastward and car $B$ is moving westward ?

• A. $15km{h}^{-1}$
• B. $45km{h}^{-1}$
• C. $60km{h}^{-1}$
• D. $105km{h}^{-1}$

Answer 1

Answer: (D)

Velocity of car $A$ w.r.t. ground
$\therefore v_{AG}=60km{h}^{-1}$
Velocity of car $B$ w.r.t. ground
$\therefore v_{BG}=-45km{h}^{-1}$
Relative velocity of car $A$ w.r.t. $B$
$v_{AB}=v_{AG}+v_{GB}$
$=v_{AG}-v_{BG}=105km{h}^{-1}\left(\because v_{GB}=-v_{BG}\right)$