Multiple choice

A boat which can moves with a speed of $5$$\mathrm { m } /$ s relative to water crosses a river of width $480$$\mathrm { m }$ flowing with a constant speed of $4$$\mathrm { m } / \mathrm { s } .$ What is the time taken by the boat to cross the tiver along the shortest path.

  1. $80$ $\mathrm { s }$
  2. $160$$\mathrm { s }$
  3. $240$$\mathrm { s }$
  4. $320$$\mathrm { s }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Shortest path means crossing perpendicular to the flow. Speed relative to ground = sqrt(5^2 - 4^2) = 3 m/s. Time = Width / Speed = 480 / 3 = 160 s.

AI explanation

To cross the river via the shortest path, the boat must steer at an angle to cancel the downstream current, so we calculate the effective crossing speed using the Pythagorean theorem: v equals the square root of (5 squared minus 4 squared), which is 3 meters per second. The time taken to cross is given by the formula time equals distance divided by speed. Substituting the river width of 480 meters and the effective speed of 3 meters per second gives a time of 160 seconds.

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