Question

Two cars $A$ and $B$ are moving with speeds $V_{A}=120\, km / hr$ and $V _{ B }=50\, km / hr$ respectively in the directions as indicated by the arrow in the figure below. What is the relative speed of the car $B$ with respect to car $A$?

• A. $70 \,km / h$
• B. $120 \,km / h$
• C. $130 \,km / h$
• D. $170\, km / h$

Answer 1

Answer: (C)

The given situation is shown in the following figure

Speed of car $A$
$v_{A}=120 \, km / h $
$\Rightarrow v_{A}=-120 \hat{i}$
Speed of car $B$
$v_{B}=50\, km / h $
$v_{B}=-50 \hat{j}$
$\therefore $ Relative speed of the car $B$ w.r.t. car $A$,
$\therefore v_{B A}=v_{B}-v_{A}=-50 \hat{j}-(-120 \hat{i})$
$=-50 \hat{j}+120 \hat{i}=120 \hat{i}-50 \hat{j} $
$\left|v_{B A}\right|=\sqrt{(120)^{2}+(-50)^{2}} $
$=\sqrt{16900}=130\, km / h$