Question

A man can row a boat with $4km/h$ in still water. If he is crossing a river where the current is $2km/h$. Width of river is $4km$. In what direction should he head the boat if he wants to cross the river in shortest time and what is this minimum time?

• A. Parallel to river current, $2$ hrs
  
• B. Perpendicular to river current, $2$ hrs
  
• C. Parallel to river current, $1$ hrs
• D. Perpendicular to river current, $1$ hrs

Answer 1

The correct option is D Perpendicular to river current, $1$ hrs

For the boat to cross the river in the shortest time, the man should head the boat in the direction perpendicular to the river current.

Given : Velocity of man wrt river, $V_{MW}=4$ $km/hr$

Velocity of river, $V_R=2$ $km/hr$

$d=4$ $km$

Minimum time taken to cross the river

$t=\frac{d}{V_{MW}}=\frac{4}{4}=1$ $hr$