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 project at the saem inclination `alpha` to the horizontal with the same speed v as shown. The time after which their separation becomes minimum is

Options

A. `d//(v cos alpha)`
B. `2d//(v cos alpha)`
C. `d//(2v cos alpha)`
D. `d//v`

Answer

C

Explanation

As the vertical component of velocity of both the particles is same.
`rArr vec(v)_(yO//O) = O`
So the distance h between h between them will be constant with time and `vec(v)_(XO//O) = 2v cos alpha`
Total distance between the particles is minimum when horizontal distance between them is zero
`rArr t = (d)/(2 v cos theta)`