A boat is moving with a velocity `v_(bw)=5 km//hr` relative to water. At time `t=0`.the boat passes through a piece of cork floating in water while moving down stream.If it turns back at time `t_(1)=30 min`.
a) when the boat meet the cork again?
b) The distance travelled by the boat during this time.

Explanation

Let `AB=d`is the distance travelled by boat along down stream in `t_(1)` sec and it returns back and it meets the cork at point `C` after `t_(2)` sec.
`:.` Let `AC=x` is the distance travelled by the cork during `(t_(1)+t_(2))` sec.
`d=(V_(B)+V_(W))t_(1)`....(1)
`d-x=(V_(B)-V_(W))t_(2)`....(2)
`x=V_(W)(t_(1)+t_(2))`....(3)
Substitute (1) and (3) in (2) we get `t_(1)=t_(2)`
`:.` The boat meets the cork again after `T=2t_(1)=60 min` and the distance `(AB+BC)` travelled by the boat before meets the cork is
`D=2d-x`
`D=2(V_(B)+V_(W))t_(1)-V_(w)2t_(1)`
`D=2V_(B)t^(1)+2V_(w)t_(1)-2V_(w)t_(1)`
`D=2V_(B)t_(1)=2xx5xx30/60=5km`