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Thread: swimmer crossing river

  1. #1
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    swimmer crossing river

    a girl wants to swim across a river 50 m wide. the river flows with a velocity of u m s-1 parallel to the banks. the girl swims at a velocity v m s^-1 . she crosses the river as quick as possible and she takes 75 seconds and she is carried down stream by 30 m. find (i) u and v (ii) how long it will take her to swim back in a straight line to her original position.

    for (i) i know she heads straight across cross the river in the shortest time. to find her j direction speed which is v i ca use distance/time so v= 50/75=2/3 m s^-1

    its the same for the river current so u= 30/75 =2/5m s^-1


    i am not sure how to do part (ii)
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  2. #2
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    Re: swimmer crossing river

    swimmer crossing river-win_20170722_10_17_12_pro.jpgClick image for larger version. 

Name:	WIN_20170722_10_17_12_Pro.jpg 
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    here is a pic for (ii), sorry it is bad.

    i think it can be solved using the sine /cosine rule. i am able to calculate a in the diagram and also 1 of the angles in the vector triangle.
    it can also be solved using relative velocity and the formula Vgr=Vg-Vr
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  3. #3
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    Re: swimmer crossing river

    She starts at position $(30,50)$ and initially swims to the origin $(0,0)$.

    The magnitudes of u and v you calculated are correct.

    Now she wants to return to her initial position ...

    Let $\theta$ be the angle she swims relative to the river bank to return to $(30,50)$. Using components ...

    $\dfrac{2}{3} \cdot t \cos{\theta} - \dfrac{2}{5} \cdot t = 30$

    $\dfrac{2}{3} \cdot t \sin{\theta} = 50$

    Solving the system for $t$, I calculate it will take about 159 seconds for her to swim back to her starting position.
    Thanks from HallsofIvy and markosheehan
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    Re: swimmer crossing river

    Thanks that's the right answer
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