Multiple choice

A $600$ meter wide river flows directly south at $4.0m/s$. A small motor boat travels at $5.0m/s$ in still water and points in such a direction so that it will travel directly east relative to the land. The time taken it takes to cross the river is closest to

  1. $67s$
  2. $120s$
  3. $150s$
  4. $200s$
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D Correct answer
Explanation

The river flows south at 4 m/s. The boat travels at 5 m/s in still water. To travel directly east, the boat must point upstream (north) to cancel the river's flow. The velocity component perpendicular to the river is sqrt(5^2 - 4^2) = 3 m/s. Time = Distance / Velocity = 600 m / 3 m/s = 200 s.

AI explanation

To travel directly east relative to the land, the boat's southward velocity component must cancel the southward river current. Using the velocity component formula, $5 \sin \theta = 4$, yielding a crossing velocity of $\sqrt{5^2 - 4^2} = 3$ m/s eastward. The time taken to cross the $600$ meter wide river is distance divided by speed, which is $600 / 3 = 200$ seconds. The result is $200s$.

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