Question

A river has a steady speed of 0.330 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point.

(a) If the student can swim at a speed of 1.10 m/s in still water, how long does the trip take?

__________ s

(b) How much time is required in still water for the same length swim?

__________ s

(c) Intuitively, why does the swim take longer when there is a current?

Answer 1

So, since the student swims 1.1 m/s in still water, he/she can swim 1.1 - 0.33 = 0.77 m/s upstream, and can swim 1.1 + 0.33 = 1.43 m/s downstream.

(a) Going upstream at 0.77 m/s --> how long does it take to swim 1000 m (1 km)

v = d/t => t = d/v => t = 1000/0.77 = 1298.7 s

Going downstream at 1.1 m/s --> how long does it take to swim 1000m (1 km)

v = d/t => t = d/v => t = 1000/1.43 = 699.3 s

So the whole trips would take:

1298.7 + 699.3 = 1998 s

(b)

If the water were still: the trip would have taken 2000/1.1 = 1818.18 s

(c)

It is completely false to think that because the swimmer is going there and back, then the two trips would be the same, because imagine if the water were flowing at the same speed as the swimmer can swim (1.1 m/s), then he/she would never get there, time would be infinite, so the faster the stream flow (in either direction) the longer the roundtrip will take.

The shortest time for the roundtrip will occur when the water is still.