Multiple choice

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

  1. Parallel to river current, $2$ hrs
  2. Perpendicular to river current, $2$ hrs
  3. Parallel to river current, $1$ hrs
  4. Perpendicular to river current, $1$ hrs
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To cross in the shortest time, the boat must head perpendicular to the current. The velocity component across the river is 4 km/h. Time = Distance / Velocity = 4 km / 4 km/h = 1 hour.

AI explanation

To cross the river in the shortest possible time, the boat must be headed perpendicular to the river current to maximize the velocity component crossing the river. This gives a crossing velocity of $4$ km/h over the width of $4$ km. The minimum time calculated is distance divided by speed, $4 / 4 = 1$ hour. The result is Perpendicular to river current, $1$ hrs.

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