Swimmer Crossing a River in Minimum Time – Rankers Physics
Topic: Kinematics
Subtopic: Relative Motion in Two Dimension

Swimmer Crossing a River in Minimum Time

A swimmer can swim with speed of \(8\text{ m/s}\) in still water. \(800\text{ m}\) wide river is flowing with speed of \(4\text{ m/s}\). Swimmer wants to cross the river in minimum time. Velocity of swimmer with respect to ground is (approximately)
9 m/s
10 m/s
12 m/s
5 m/s

Solution:

For minimum crossing time, the swimmer must head perpendicular to the river bank. The net ground velocity is the vector sum of swimmer's velocity and river velocity: \(v_g = \sqrt{v_{\text{sw}}^2 + v_r^2} = \sqrt{8^2 + 4^2} = \sqrt{80} \approx 8.94\text{ m/s} \approx 9\text{ m/s}\).

Leave a Reply

Your email address will not be published. Required fields are marked *