Question

Two cars $A$ and $B$ start moving from the same point with same velocity $v=5km/$ minute. Car $A$ moves towards north and car $B$ is moving towards east. What is the relative velocity of $B$ with respect to $A$ ?

• A. $5\sqrt{2}km/min$ towards south-east
• B. $5\sqrt{2}km/min$ towards north-west
• C. $5\sqrt{2}km/min$ towards south-west
• D. $5\sqrt{2}km/min$ towards north-east

Answer 1

Answer: (A)

The velocity of car $A$ and car $B$ are represented by the vectors as shown in the figure.

Given : $v_A=v_B=v=5km/$ minute
The relative velocity of car $B$ w.r.t to car $A$ is given by
${\vec{v}}_{BA}={\vec{v}}_B-{\vec{v}}_A$
$\left|{\vec{v}}_{BA}\right|=\sqrt{v_B^2+{\left(-v_A\right)}^2+2\left(v_B\right)\left(-v_A\right)\cos \left(90^{\circ }\right)}$
$=\sqrt{(5{)}^2+(-5{)}^2+(0)}=5\sqrt{2}km$ minute
The direction $\beta$ is given by
$\tan \beta =\frac{v_B}{v_A}=\frac{5}{5}=1$
or $\beta =45^{\circ }$ in south-east