A particle `P` is initially at a distance `c'=16m` from a fixed point `O`. The particle `P` moves with a velocity `vecv=5overset(^^)(PO)+3hati`. Where `overset(^^)(PO)` is a unit vector from `P` to `O` at any time `t`. Initially `overset(^^)(PO)` is perpendicular to `hati`. Find the time in seconds after which point `P` meets point `O`.

Explanation

`-(dr)/(dt)=5-3costheta`
`int_(16)^(0)-dr=int_(0)^(t)(5-3costheta)dt`
`16=5t-3int_(0)^(t)costheta dt`
`int_(0)^(t)(3-5costheta)dt=0rArrint_(0)^(t)costheta dt=(3t)/(5)`
`16=5t-(9t)/(5)`
`t=5sec`.