Jon, the swimmer.

Classical Mechanics Level 3

A 240 m wide river is flowing downwards at a rate of 1800 m/h and Jon, the swimmer can swim at a rate of 3600 m/h, who wishes to reach a point just opposite.

How long will he take in reaching the point?

Details and assumptions:

  • Submit your answer to 3 decimal places.

  • Give your answer in hours.


The answer is 0.077.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Arjen Vreugdenhil
Dec 14, 2017

Jon's swimming speed of 3600 m/h is relative to the water. If he would cross the river as fast as he could, he would therefore end up downstream.

To reach the point directly across, Jon must swim upstream (relative to the water). His upstream velocity component must be 1800 m/h. Using Pythagoras we find the component perpendicular to the flow: v 2 = 360 0 2 − 180 0 2 ∴ v = 3 118 m / h . v^2 = 3600^2 - 1800^2\ \ \ \therefore\ \ \ v = \SI{3118}{m/h}. The time Jon needs to cross is therefore 240 m 3 118 m / h = 0.077 0 h . \frac{\SI{240}{m}}{\SI{3118}{m/h}} = \SI{0.0770}{h}.

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