Question

Two cars $A$ and $B$ are moving with speeds $V_A=120km/hr$ and $V_B=50km/hr$ 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. $70km/h$
• B. $120km/h$
• C. $130km/h$
• D. $170km/h$

Answer 1

Answer: (C)

The given situation is shown in the following figure

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