Question

Two balls $A$ and $B$ are projected simultaneously as shown in the figure. Find the closest distance between the balls.

• A. $30\text{m}$
• B. $50\text{m}$
• C. $60\text{m}$
• D. $80\text{m}$

Answer 1

The correct option is B $50\text{m}$

$\because$ Relative acceleration between the balls is zero.
$\therefore$ Bodies are moving with constant velocities w.r.t each other.
Considering $B$ to be at rest and finding $\overrightarrow{V_{AB}}$ velocity of $A$ w.r.t $B$.

$\overrightarrow{V_{AB}}=(20+20\sin {30}^{\circ })\hat{i}+\left(20\cos {30}^{\circ }\right)\hat{j}\Rightarrow V_{AB}=30\hat{i}+10\sqrt{3}\hat{j}$ and the angle made with the horizontal is
$\tan \theta =\frac{10\sqrt{3}}{30}\Rightarrow \theta ={30}^{\circ }$

Shortest distance between the balls $BC=AB\sin {30}^{\circ }=100\left(\frac{1}{2}\right)=50\text{m}$

Hence option B is the correct answer