Question

A swimmer, capable of swimming at a speed of 1.0 m/s in still water (i.e., the swimmer can swim with a speed of 1.0 m/s relative to the water), starts to swim directly across a 3.0-km-wide river. However, the current is 0.91 m/s, and it carries the swimmer downstream.
(a) How long does it take the swimmer to cross the river?
(b) How far downstream will the swimmer be upon reaching the other side of the river?

Answer 1

If the current takes him downstream we must find the resultant vector of the velocities: $V res= \sqrt{1^{2}+0.91^{2} } = \sqrt{1.8281}= 1.3520747$ Then if the river is 3000 m-wide the swimmer will have to pass:
 1.3520747 · 300 = 4056.14 m                t = 4056.14 m : 1 m/s
a ) It takes 4056.15 seconds ( 1 hour 7 minutes and 36 seconds ) to cross the river.  
b ) 0.91 · 3000 = 2730 m
He will be 2730 m downstream.