relative motion

Question

Swimmer speed relative water 2 m/s; river speed 1 m/s. Width 100 m. Minimum crossing time is:

RankGuru · Accepted Answer

To cross the river in minimum time, the swimmer must swim directly perpendicular to the river current (parallel to the width). 
The time taken to cross is determined only by the component of velocity perpendicular to the river banks ($v_y$).
$t_{min} = \frac{	ext{Width}}{v_{swimmer}} = \frac{100 	ext{ m}}{2 	ext{ m/s}} = 50 	ext{ s}$.
Note: While the swimmer will be carried downstream (drift) by the river current, this does not affect the time required to cover the $100 	ext{ m}$ width.

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