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.