Question

A motor boat going downstream overcame a raft at a point A; $\tau =60min$ later it turned back and after some time passed the raft at a distance $l=6.0km$ from point A. Find the flow velocity assuming the duty of the engine to be constant.

Answer 1

Let ${\nu }_0$ be the stream velocity and ${\nu }^{{}^{\prime }}$$thevelocityofmotorboatwithrespecttowater.Themotorboatreachedpoint$B$whilegoingdownstreamwithvelocity$(\nu_0+ \nu^{'})$andthenreturnedwithvelocity$(\nu^{'}- \nu_0)$andpassedtheraftatpoint$C$.Let$t$bethetimefortheraft(whichflowswithstreamwithvelocity$\nu_0$)tomovefrompoint$A$to$C$,duringwhichthemotorboatmovesfrom$A$to$B$andthenfrom$B$to$C$

Therefore

$\frac{l}{{\nu }_0}=\tau +\frac{({\nu }_0+{\nu }^{{}^{\prime }})\tau -l}{(v^{{}^{\prime }}-{\nu }_0)}$

on solving we get ${\nu }_0=\frac{1}{2\tau }$