In the 2016 olympics in rio, after the 50 m freestyle competition, a problem with the pool was found. in lane 1there was a gentle 1.2 cm/s current flowing in the direction that the swimmers were going, while in lane 8there was a current of the same speed but directed opposite to the swimmers' direction. suppose a swimmer could swim the 50.0 m in 25.0 s in the absence of any current. how would the time it took the swimmer to swim 50.0 m change in lane 1?
enter negative value if the swimmer would be faster and positive value if the swimmer would be slower. part b
how would the time it took the swimmer to swim 50.0 m change in lane 8?
enter negative value if the swimmer would be faster and positive value if the swimmer would be slower.

A) -0.15 s

First of all, we need to velocity of the swimmer in absence of current. This is given by:

where

d = 50.0 m

t = 25.0 s

Substituting,

In lane 1, the velocity of the current is

where the + sign means it is in the same direction as the swimmer. Therefore, the net velocity of the swimmer in lane 1 will be

And so, the time the swimmer will take to cover the 50.0 m will be:

So, the time would change by

which means that the swimmer will be 0.15 s faster.

B) +0.15 s

To solve this part, we just need to consider that the current goes in the opposite direction, so its velocity actually is:

where the negative sign indicates the opposite direction.

So, the net velocity of the swimmer in lane 8 is

And so, the time the swimmer will take to cover the 50.0 m will be:

So, the time would change by

which means that the swimmer will be 0.15 s slower.

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