Swimmer Shortest Path Angle – Rankers Physics

Uncategorized: Practice Problem & Solution

The speed of a swimmer in still water is \(20 text{ m/s}\). The speed of river water is \(10 text{ m/s}text{ 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: (2019)}\
\(30°text{ west}\)
\(0°\)
\(60°text{ west}\)
\(45°text{ west}\)

Solution Explained:

To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:

Concept: Relative velocity for shortest path across a river.
Formula: \(sin theta = v_r / v_s\), where \(theta\) is the angle upstream.
Given \(v_s = 20text{ m/s}\), \(v_r = 10text{ m/s}\).
For the shortest path, \(sin theta = 10/20 = 1/2\). Thus, \(theta = 30°\).
The direction is \(30°text{ west of north}\).

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