A man crosses a river in a boat. If he crosses the river in minimum time he takes 10 minutes with a drift $120 m$. If he crosses the river taking
shortest path, he takes 12.5 minute:(Assume $v_{b/r}>v_r$)

Shortest time                                         Shortest path

$$\begin{gathered} 10 =\frac{w}{\sqrt{{\left(v_{br}\right)}^2-{\left(v_r\right)}^2}} ......\left(1\right) 12.5=\frac{w}{v_{br} \cos \theta }.......\left(3\right) \\ 120=10\times v_{r } ..................\left(2\right) \Rightarrow 12.5=10 \sec \theta \\ {v}_r=12 m/min \\ \Rightarrow \cos \theta =\frac{4}{5} \\ Also v_{br}=\frac{v_r}{\sin \theta }=\frac{12}{\left(3/5\right)}m/s=20 m/s \\ and w =12.5\times 20\times \frac{4}{5}m/s =200 m \end{gathered}$$