physics

A lifeguard who can swim at 1.2 m/s in still water wants to reach a dock positioned perpendicularly directly across a 550 m wide river.
If the current in the river is 0.80 m/s, how long will it take the lifeguard to reach the dock?
If instead she had decided to swim in such a way that will allow her to cross the river in a minimum amount of time, where would she land relative to the dock?

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asked by grey
  1. Her resultant speed is perpendicular to the flow of the river.
    Thus resultant velocity, using Pythagoras theorem,
    V=√(1.2²-0.8²)
    =√(0.8)
    =0.8944 m/s

    Time to cross river
    =550m/0.8944 m/s
    =614.9 s
    =10 minutes 15 seconds, approx.

    to cross as rapidly a possible, the crossing speed is exactly 1.2 m/s,
    time = 550/1.2
    = 458.3 s
    = 7min. 38.3 sec.

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    posted by MathMate

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