Question

Two particles A and B are projected simultaneously in the direction shown in figure with velocities $E_A=20m/s$ and $v_B=10m/s$ respectively. They collide in air after $\frac{1}{2}s.$ Find
(a) the angle $\theta$
(b) the distance $x$.

Answer 1

For collision there $x$ and $y$ co-ordinate should be same.

$y=v_A\sin \theta t-\frac{1}{2}g{t}^2=v_{B}t-\frac{1}{2}g{t}^2$ at $t=\frac{1}{2}$

$⟹v_A\sin \theta =v_B$

$⟹\sin \theta =\frac{v_B}{v_A}=\frac{10}{20}=\frac{1}{2}$

$⟹\theta ={30}^o$

$x_A=x_B$

$⟹x=v_A\cos \theta t=20\times \frac{\sqrt{3}}{2}\times \frac{1}{2}$

$⟹x=5\sqrt{3}s$