Question

Two particles are projected from the top of two towers as shown in the figure. Find the time at which they collide. Both particles are projected simultaneously at $t=0$ second.

• A. 1 sec
• B. 2 sec
• C. 3 sec
• D. 4 sec

Answer 1

The correct option is B 2 sec

Taking upward direction as positive
For particles to collide
$(S_{AB}{)}_y=120-80=40$
$u_{AB}=u_A-u_B=100\sin {30}^{\circ }-30$
Relative acceleration, $a=g-g=0$
$(S_{AB}{)}_y=(u_{AB}{)}_{y}t+\frac{1}{2}\left(a_{AB}\right)y{t}^2$
$40=(100\sin {30}^{\circ }-30)t+0$
$40=20t$
$\Rightarrow t=2\text{seconds}$