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28 May, 13:27

A cowboy at a dude ranch fills a horse trough that is 1.53 m long, 61 cm wide, and 42 cm deep. He uses a 2.0-cm-diameter hose from which water emerges at 1.66 m/s. How long does it take him to fill the trough?

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  1. 28 May, 17:02
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    It takes him 751.39 seconds to fill the trough

    Explanation:

    The flow rate = Velocity of the hose * cross sectional area of the hose.

    Q = V*A ... Equation 1

    Where Q = flow rate, V = velocity, A = cross sectional area.

    Given: V = 1.66 m/s,

    A = πd²/4, Where d = 2.00 cm = 0.02 m.

    Therefore, A = 3.143 (0.02) ²/4 = 0.0003143 m²

    Substituting these values into equation 1

    Q = 1.66*0.0003143

    Q = 0.0005217 m³/s.

    Time taken to fill the trough = Volume of the trough/flow rate.

    t = V/Q ... Equation 2.

    Where V = volume of the trough, Q = flow rate.

    Given: Q = 0.0005217 m³/s, V = length*width*height = l*w*h, l = 1.53 m, w = 61 cm = 0.61 m, h = 42 cm = 0.42 m.

    V = 1.53*0.61*0.42 = 0.392 cm³

    Substituting these value into equation 2,

    t = 0.392/0.0005217

    t = 751.39 seconds.

    Thus it takes him 751.39 seconds to fill the trough
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