Question

Two bodies $A$ and $B$ are travelling with constant velocities of $20\text{m/s}$ and $30\text{m/s}$ in East and North directions. The relative velocity of $A$ with respect to $B$ is

• A. $10\sqrt{13}\text{m/s}$ in the E-S quadrant
• B. $10\sqrt{13}\text{m/s}$ in the E-N quadrant
• C. $10\sqrt{13}\text{m/s}$ in the W-S quadrant
• D. $10\sqrt{13}\text{m/s}$ in the W-N quadrant

Answer 1

The correct option is A $10\sqrt{13}\text{m/s}$ in the E-S quadrant

${\overrightarrow{v}}_{AB}={\overrightarrow{v}}_A-{\overrightarrow{v}}_B=20\hat{i}-30\hat{j}$
$\left|{\overrightarrow{v}}_{AB}\right|=\sqrt{{20}^2+{30}^2}=10\sqrt{13}\text{m/s}$
The direction of the resultant is given by
$\tan \theta =\frac{-30}{20}=-56.3$
The negative angle comes in the East-South quandrant. Hence the correct option is (a).