Multiple choice

A river is flowing at 3 $m\;{s^{ - 1}}$ .A man can swim in still water at a speed of 6 $m\;{s^{ - 1}}$. the angle with the bank at which the swimmer should start, so that he may cross the river along the shortest possible distance is.

  1. ${120^0}\;up\;stream$
  2. ${60^0}\;up\;stream$
  3. ${30^0}\;down\;stream$
  4. ${60^0}\;down\;stream$
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A Correct answer
AI explanation

To cross the river along the shortest possible distance, the swimmer must head at an angle theta upstream such that the upstream component of his velocity exactly cancels the river's flow. This requires the equation 6cos(theta) = 3, meaning cos(theta) equals 0.5 and the angle theta is 60 degrees upstream from the bank. Since the options are measured from the direction of the river flow, the upstream angle is 180 - 60 = 120 degrees. The swimmer should start at 120 degrees upstream.

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