Question

Two particles are projected simultaneously from two points, O and O' such that d is the horizontal distance and h is the vertical distance between them. They are projected at the same inclination a to the horizontal with the same speed v. The time after which their separation becomes minimum is

• A. $\frac{d}{\text{v cos}\alpha }$
• B. $\frac{2d}{\text{v cos}\alpha }$
• C. $\frac{d}{\text{2v cos}\alpha }$
• D. $\frac{d}{v}$

Answer 1

The correct option is C

$\frac{d}{\text{2v cos}\alpha }$

As the vertical component of velocity of both the particles is same.

$\Rightarrow {\overrightarrow{v}}_{\frac{yO}{O^{{}^{\prime }}}}=0$

So the distance h between them will be constant with time and ${\overrightarrow{v}}_{\frac{xO}{O^{{}^{\prime }}}}=2v\text{cos}\alpha$

Total distance between the particles is minimum when horizontal distance between them is zero.

$\Rightarrow \text{t}=\frac{\text{d}}{2v\text{cos}\alpha }$