Multiple choice

A boat is to cross a river of width 500 m. The velocity of the river flow is 5 kmph and the velocity of the boat is 10 krnph. The angle at which the boat is to be rowed with the direction of river flow velocity so that the boat can cross the river along shortest path is

  1. $120^o$
  2. $135^o$
  3. $150^o$
  4. $60^o$
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A Correct answer
Explanation

For the shortest crossing path, the resultant velocity must be perpendicular to the river flow. The boat's upstream velocity component must therefore cancel the river velocity, so 10 cos(theta) + 5 = 0. Hence cos(theta) = -1/2 and theta = 120 degrees.

AI explanation

For the boat to cross along the shortest path, its upstream velocity component must cancel the river flow, so $10 \sin \theta = 5$ where $\theta$ is the angle with the perpendicular. This gives $\sin \theta = 1 / 2$, meaning $\theta = 30^\circ$ with the perpendicular. The angle with the direction of the river flow is $90^\circ + 30^\circ = 120^\circ$. The result is $120^\circ$.

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