Question

Particles $A$ and $B$ are moving as shown in the figure. At $t=0$, both the particles are at same horizontal level. Will the particles collide in the air ? If yes, then find the angle $\theta$ made by velocity of particle $B$ from horizontal.

• A. Yes, ${30}^{\circ }$
• B. Yes, ${60}^{\circ }$
• C. Yes, ${45}^{\circ }$
• D. particles will not collide

Answer 1

The correct option is A Yes, ${30}^{\circ }$

For particles to collide relative velocity component in vertical direction $\left(y\right)$ should be Zero $\&$ the seperation between particles should decrease.

Hence,
$10\sin \theta =5$
Or, $\sin \theta =\frac{5}{10}=\frac{1}{2}$
$\theta ={30}^{\circ }$
Now velocity of $B$ w.r.t $A$ along $x-$direction is,
$(v_{BA}{)}_x=(v_B{)}_x-(v_A{)}_x$
$(v_{BA}{)}_x=10\cos {30}^{\circ }-9=5\sqrt{3}-9$
$\therefore (v_{BA}{)}_x=-0.34\text{m/s}$

$\Rightarrow (v_{BA}{)}_x$ is directed along $-vex$ direction, hence separation between $A\&B$ will decrease and they will collide.