Question

In the figure shown, the two projectiles are fired simultaneously. Find the minimum distance between them during their flight?

Answer 1

$v_{A{B}_x}=10\sqrt{3}-(-10\sqrt{3})$
$=20\sqrt{3}\text{m/s}$
$v_{A{B}_y}=30-10=20\text{m/s}$
${\overrightarrow{v}}_{AB}={\overrightarrow{v}}_A-{\overrightarrow{v}}_B\Rightarrow v_{AB}=20\sqrt{3}\hat{i}+20\hat{j}$
$\because \tan \theta =\frac{\text{component of}y}{\text{component of}x}$
$\tan \theta =\frac{20}{20\sqrt{3}}$
$\tan \theta =\frac{1}{\sqrt{3}}\Rightarrow \theta ={\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
$\Rightarrow \theta ={30}^{\circ }$
$x=20\sin {30}^{\circ }$
$x=10\text{m}$