Question

The speed of a swimmer in still water is \(20 m/s\). The speed of river water is \(10 m/s\) and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by:

• A. 30° wes
• B. 0°
• C. 60° west
• D. 45° west

Answer 1

The Correct Option is A

To solve this problem, we need to consider the relative velocities and determine the direction in which the swimmer should swim to minimize the distance while crossing the river.

The swimmer's speed in still water is 20 \, \text{m/s}. The river's water flows east at 10 \, \text{m/s}. To cross the river in the shortest path (i.e., directly north), the swimmer must swim against the river's current.

We need to find the angle at which the swimmer should swim concerning the north to achieve this path. Let's use vector analysis to solve it:

1. Let the speed of the swimmer in still water be V_s = 20 \, \text{m/s}.

2. Let the speed of the river be V_r = 10 \, \text{m/s}, flowing east.

3. To cross straight, the swimmer must compensate for the river drift. This requires swimming in a northwest direction.

4. From the north direction, let the angle be \theta west. The component of the swimmer's velocity against the river's drift (east) must equal the river speed.

   The swimmer’s velocity component against the river: V_s \sin \theta = V_r.
   Thus, 20 \sin \theta = 10.

   Solve for \theta:

   \sin \theta = \frac{10}{20} = \frac{1}{2}

   The angle \theta for which \sin \theta = \frac{1}{2} is 30^\circ.

Therefore, the swimmer should swim at an angle of 30^\circ west of north to cross the river along the shortest path.

The correct answer is 30^\circ west.