Answer to Question #95637 in Mechanics | Relativity for sean

Question

In the 2016 Olympics in Rio, after the 50 m freestyle competition, a problem with the pool was found. In lane 1 there was a gentle 1.2 cm/s current flowing in the direction that the swimmers were going, while in lane 8 there 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?

Answer 1

$$t'=\frac{d}{V+u}$$

$$V=\frac{d}{t}$$

Thus, the time decreases by

$$t-t'=t-\frac{d}{\frac{d}{t}+u}=t\left(1-\frac{1}{1+\frac{ut}{d}}\right )$$

$$t-t'=25\left(1-\frac{1}{1+\frac{(0.012)(25)}{50}}\right )=0.15\ s$$