A river of width 200 m is flowing from west to east with a speed of $18 \mathrm{~km} / \mathrm{h}$.

Question

A river of width 200 m is flowing from west to east with a speed of $18 \mathrm{~km} / \mathrm{h}$. A boat, moving with speed of $36 \mathrm{~km} / \mathrm{h}$ in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are $\_\_\_\_$ and $\_\_\_\_$ respectively.

Professor PC Thomas Classes · Answer

River speed $u = 18	ext{ km/h} = 5	ext{ m/s}$ and boat speed $v = 36	ext{ km/h} = 10	ext{ m/s}$. To cross the river in minimum time, the boat must be rowed perpendicular to the river flow. Time taken to cross one way is $t = \frac{d}{v} = \frac{200}{10} = 20	ext{ s}$. For a round trip, total time is $20 + 20 = 40	ext{ s}$. The boat drifts down the river due to the current. Total drift along the bank is $x = u 	imes t_{total} = 5 	imes 40 = 200	ext{ m}$.