Question

Particle $A$ moves along $x$-axis with a uniform velocity of magnitude $10{\text{ms}}^{-1}$. Particle B moves with uniform velocity of $20{\text{ms}}^{-1}$ along a direction making an angle of ${60}^{\circ }$ with the positive direction of $x$-axis. The relative velocity of $B$ with respect to that of $A$ is

• A. $10{\text{ms}}^{-1}$ along $x$ - axis
• B. $10\sqrt{3}{\text{ms}}^{-1}$ along $y$ - axis (perpendicular to $x$ - axis)
• C. $10\sqrt{5}{\text{ms}}^{-1}$ along the bisection of the velocities of $A$ and $B$
• D. $30{\text{ms}}^{-1}$ along negative $x$ - axis

Answer 1

The correct option is B $10\sqrt{3}{\text{ms}}^{-1}$ along $y$ - axis (perpendicular to $x$ - axis)


Particle $A$ is moving along the $x$ - axis. Hence it has only $\hat{i}$ component of direction.
${\overrightarrow{v}}_A=10\hat{i}$
Particle $B$ has both $X$ and $Y$ components.
${\overrightarrow{v}}_B=20\cos 60\hat{i}+20\sin 60\hat{j}=20\left(\frac{1}{2}\right)\hat{i}+20\left(\frac{\sqrt{3}}{2}\right)\hat{j}=10\hat{i}+10\sqrt{3}\hat{j}$
The velocity of $B$ with respect to $A$ =
${\overrightarrow{v}}_{AB}={\overrightarrow{v}}_B-{\overrightarrow{v}}_A=10\sqrt{3}\hat{j}$
Hence, the correct answer is option (b)