The distance between two moving particles `P` and `Q` at any time is a.If `v_(r)` be their relative velocity and if `u` and `v` be the components of `v_(r)`, along and perpendicular to `PQ`.The closest distance between `P` and `Q` and time that elapses before they arrive at their nearest distance is

Options

A. `(a(v+v_(r)))/(v)`
B. `(1+(v_(r))/(u))^(2)`
C. `(av)/((v+v_(r))),a(1+(u)/(v_(r)))^(2)`
D. `(av_(r))/(v),(av_(r))/(u^(2))`

Answer

d

Explanation

Assuming P top be at rest, particle Q is moving with velocity `v_(r)`, in the direction shown in figure. Components of `v_(r)` along and perpendicu lar to PQ are u and v respectively. In the figures.
`sin alpha=(v)/(v_(r)),cos alpha=(v)/(v_(r))`
The closest dstance between the particles is PR.
`s_("min")=PR=PQ cos alpha=(a)((v)/(v_(r)))rArt_("min")=(av)/(v_(r))`

`t=(OR)/(v_(r))=((PQ)sin alpha)/(v_(r))=(a)((v)/(v_(r)))/(v_(4))=(au)/(v_(r)^(2))`