Two particles are projected from two high rise buildings simultaneously as shown then find minimum distance between particles.

Explanation

This can be solved by considering reference frame attached to one of the particles. (By relative motion) Velocity of A w.r.t. B `" "vec(v)_(AB)=vec(v)_(A)-vec(v)_(B)`
`=(sqrt(2)hat(i)+sqrt(2)hat(j))-(-7sqrt(2)hat(i)+7sqrt(2)hat(j))`
`=8sqrt(2)hat(i)-6sqrt(2)hat(j)`
Dir. of `vec(v)_(AB)" "tan alpha=(-6sqrt(2))/(8sqrt(2))=(-3)/4`
`alpha=37^(@)` (downward from horizontal)
from
`tan 37^(@)=(AC)/(CD)=3/4`
`CD=(9xx4)/3=12 m" " :' " "BD=27-12=15m`
From
`(BP)/(BD)=sin 37^(@)=3/5`
`(BP)/15=3/5 rArr BP=9 m`