Multiple choice

A river is flowing at a speed of 3 m/s doe east. A boat, whose speed in still water is 6 m/s, sis steered in the direction due to the north. Find the angle made by the resultant velocity of summer w.r.t river flow.

  1. $30^\circ$
  2. $37^\circ$
  3. $53^\circ$
  4. $63.4^\circ$
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D Correct answer
Explanation

The river contributes 3 m/s eastward and the boat contributes 6 m/s northward. Therefore, tan(theta) = 6/3 = 2, so theta is approximately 63.4 degrees from the river flow.

AI explanation

The boat's velocity across the river is 6 m/s and the river current pushes it east at 3 m/s, forming a right-angled triangle where the angle of the resultant velocity with the east direction is theta. The tangent of this angle is the ratio of northward velocity to eastward velocity, so tan(theta) = 6/3 = 2. Evaluating the inverse tangent gives theta = arctan(2), which is approximately 63.4 degrees. The result is 63.4 degrees.

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