Question

Two particles are moving with velocities $v_1$ and $v_2$. Their relative velocity is the maximum, when the angle between their velocity vectors is

• A. zero
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer 1

The correct option is D $\pi$

The relative velocity ${\overrightarrow{v}}_r$ is given by,
${\overrightarrow{v}}_r={\overrightarrow{v}}_1-{\overrightarrow{v}}_2$
$|{\overrightarrow{v}}_r|=\sqrt{v_1^2+v_2^2-2v_1{v}_{2}cos\theta }$
So, clearly $|{\overrightarrow{v}}_r|$ will be maximum when $cos\theta =-1⟹\theta =\pi$
$\Rightarrow v_r=v_1+v_2$
Thus, for maximum relative velocity angle between velocity vectors should be $\pi$