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

The Correct Option is C

$\vec{r}_{1} =vt \hat{i} -\frac{1}{2} gt^{2} \hat{j}, \vec{r}_{2} =vt \left(-\hat{i}\right)-\frac{1}{2}gt^{2} \hat{j}$
$\vec{r_{1}} \overrightarrow{r_{2}} =0 , \Rightarrow -v^{2}t^{2} +\frac{1}{4}g^{2}t^{4} =0,$
$v^{2}=\frac{1}{4}g^{2}t^{2}, v=\frac{gt}{2},$
$\Delta x =2vt =2\times v\times\frac{2v}{g} =\frac{4v^{2}}{g}$