Question

Two particles are simultaneously projected in the horizontal direction from a point $P$ at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude v each. The separation between the particles at a time when their position vectors (drawn from the point P) are mutually perpendicular, is

• A. $\frac{v^2}{2g}$
• B. $\frac{v^2}{g}$
• C. $\frac{4v^2}{g}$
• D. $\frac{2v^2}{g}$

Answer 1

Answer: (C)

$\frac{4v^2}{g}$

${\overrightarrow{r}}_1=vt\hat{i}-\frac{1}{2}g{t}^2\hat{j},{\overrightarrow{r}}_2=vt(-i)-\frac{1}{2}g{t}^2\hat{j}$
$\overrightarrow{r_1}.\overrightarrow{r_2}=0,\Rightarrow -v^2{t}^2+\frac{1}{4}{g}^2{t}^4=0$
$v^2=\frac{1}{4}{g}^2{t}^2,v\frac{gt}{2}$
$△x=2vt=2\times v\times \frac{2v}{g}=\frac{4v^2}{g}$