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Swimming across a river question

  1. Jul 30, 2010 #1
    1. The problem statement, all variables and given/known data

    A swimmer is standing on the west bank of a river 600 m wide. The current in the river is 3.0m/s and the swimmer can swim 5.0 m/s in still water.

    a) If the swimmer swims due east, what is the time it takes to get across the river?
    b) What is the minimum time to get across the river?
    c) Where does the swimmer end up when he travels in minimum time?


    2. Relevant equations

    t = d/v

    3. The attempt at a solution

    Alright, apparently I did it wrong, but I can't figure out where my logic went wrong. I had this question on my exam today, and afterward, everyone I talked to did it differently from me, so I know I'm wrong.

    a) Okay, so I figured if the swimmer points himself directly across the river, the current would push him down. So, thinking of it as a triangle, I used the velocities to find the angle, then the angle and the width of the river to find the hypoteneuse distance, the distance I thought he would travel. Then I did d / v to get time as 140 seconds.

    Apparently I should have used the width of the river (600 m)...which I did for:

    b) Okay, so for minimum time, I thought this would occur if the swimmer travels the exact width of the river meaning he has to start at an angle. So if he started at the angle I found in part a, he would end up going directly across. So I did t = 600 / v to get 120 seconds.

    Apparently the answer to this should have been that the minimum time is what I found in a) (which should have been 120).

    c) Well I said with the minimum time, the swimmer would have made it directly across and his position would be opposite from where he started.

    Obviously if a and b were wrong, that is too.

    Can someone help me see where I went wrong with the logic? D:
    I know this question is pretty easy and straightforward, but I tend to mess those ones up the most...
     
  2. jcsd
  3. Jul 30, 2010 #2

    ehild

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    a. An observer standing on the bank of the river sees him swimming due East. The swimmer arrives at a place directly across his starting point. This means that the resultant of the swimmer's velocity and the velocity of the river points to East. So the swimming velocity has an upstream component. What is the eastward component?
    b. The swimmer swims with all his strength across the river eastward, looking at his compass ( he was clever and took one with him). How long does it take to cross the river now?
    c. During this time the flow carried him downstream. How far?
     
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