Question

A swimmer can swim at \(5\,\text{m s}^{-1}\) in still water. River flows at \(3\,\text{m s}^{-1}\). To cross the river in shortest time, the angle with respect to the perpendicular to the flow is

• A. \(0^\circ\)
• B. \[ \sin^{-1}\left(\frac{3}{5}\right) \]
• C. \[ \tan^{-1}\left(\frac{3}{5}\right) \]
• D. \(90^\circ\)

Hint:

For \textbf{minimum time crossing}, always swim perpendicular to the river flow. For \textbf{reaching the point directly opposite}, swim at an upstream angle so that the river drift is compensated.

Answer 1

The Correct Option is A

Concept: Minimum crossing time requires maximum perpendicular velocity component. Swimmer's speed \(v=5\) m/s; perpendicular component = \(5\cos\theta\). Minimize time \(t = d/(5\cos\theta)\) by maximizing \(\cos\theta\). \(\cos\theta_{\max}=1\) at \(\theta=0^\circ\).

Step 1: Write the final answer. \(\boxed{\theta=0^\circ}\)