Question

Two particles $A$ and $B$ are projected simultaneously from the top of two towers as shown in the figure. After what time from their projection will they collide?

• A. $1\text{sec}$
• B. $2\text{sec}$
• C. $3\text{sec}$
• D. $4\text{sec}$

Answer 1

The correct option is B $2\text{sec}$

Taking downward as positive direction. For the particles to collide Relative displacement in y- direction should be '0'.
So,
$(S_{rel}{)}_y=0$ and $(S_{rel}{)}_x=150$
$(S_{rel}{)}_x=(u_{rel}{)}_{x}t+\frac{1}{2}(a_{rel}{)}_x{t}^2$
$150=(45\sin {37}^{\circ }+60\sin {53}^{\circ })t$ $(\because (a_{rel}{)}_x=0)$
$150=(27+48)t$
$\Rightarrow t=2\text{sec}$