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21 April, 20:20

You are working as an assistant to a landscape architect, who is planning an artificial waterfall in a city park. Water flowing at 1.93 m/s will leave the end of a horizontal channel at the top of a vertical wall h = 3.05 m high, and from there it will fall into a pool (see the figure below) (a) The architect has asked you to determine if the space behind the waterfall will be wide enough for a pedestrian walkway. (Enter the maximum width, in meters, of a walkway behind the waterfall.) (b) To sell her plan to the city council, the architect wants to build a model to standard scale, which is one-twelfth actual size. She asks you to design and build the model, with the important question being: how fast (in m/s) should the water flow in the channel in the model? m/s

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  1. 21 April, 20:49
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    a) width=1.20m

    b) The speed of the model will be 0.193m/s

    Explanation:

    Using Y (t) = -gt^2+Voy + yo

    g=9.8m/s

    Vo=0 at t=0

    Vox=1.93m/s

    yo = 3.05m

    Y (t) = (-1/2) 9.8t^2+3.05

    Y (t) = - 4.9 + 3.05

    0 = - 4.9t^2 + 3.05

    t = sqrt (3.05/4.9)

    t = 0.62second

    Xmax = Voxt = 1.93*0.62=1.20m

    b) The model is 1/12

    Therefore velocity of model = 1/2*1.2*1.93

    =0.193m/s
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