Answer to Question #95637 in Mechanics | Relativity for sean

Question #95637
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?
1
Expert's answer
2019-10-02T09:37:39-0400
t=dV+ut'=\frac{d}{V+u}

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

Thus, the time decreases by


tt=tddt+u=t(111+utd)t-t'=t-\frac{d}{\frac{d}{t}+u}=t\left(1-\frac{1}{1+\frac{ut}{d}}\right )


tt=25(111+(0.012)(25)50)=0.15 st-t'=25\left(1-\frac{1}{1+\frac{(0.012)(25)}{50}}\right )=0.15\ s


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