Question

Two Cars $A$ and $B$ are travelling with constant velocities of $10\text{m/s}$ and $20\text{m/s}$ respectively along straight lines making an angle of $60°$ with each other. The magnitude of relative velocity of $A$ with respect to $B$ is

• A. $10\sqrt{3}\text{m/s}$
• B. $20\text{m/s}$
• C. $10\text{m/s}$
• D. $20\sqrt{3}\text{m/s}$

Answer 1

The correct option is A $10\sqrt{3}\text{m/s}$

Magnitude of relative velocity of $A$ with respect to $B$,
$\left|{\overrightarrow{v}}_{AB}\right|=|{\overrightarrow{v}}_A-{\overrightarrow{v}}_B|$
Using parallelogram law of vector addition,
$\left|{\overrightarrow{v}}_{AB}\right|=\sqrt{v_A^2+v_B^2-2v_A{v}_B\cos \theta }$
$=\sqrt{{10}^2+{20}^2-2\times 10\times 20\cos 60°}$
$=10\sqrt{3}\text{m/s}$