A fireperson is 50 m from a burning building and directs a stream of water from a fire hose at an angle of 300 above the horizontal. If the

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A fireperson is 50 m from a burning building and directs a stream of water from a fire hose at an angle of 300 above the horizontal. If the initial speed of the stream is 40 m/s the height that the stream of water will strike the building is

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Mộc Miên 3 years 2021-08-08T10:51:52+00:00 1 Answers 9 views 0

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  1. thienhuong
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    2021-08-08T10:52:53+00:00
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    Answer:

    We can think the water stream as a solid object that is fired.

    The distance between the fireperson and the building is 50m. (i consider that the position of the fireperson is our position = 0)

    The angle is 30 above the horizontal. (yo wrote 300, but this has no sense because 300° implies that he is pointing to the ground).

    The initial speed of the stream is 40m/s.

    First, using the fact that:

    x = R*cos(θ)

    y = R*sin(θ)

    in this case R = 40m/s and θ = 30°

    We can use the above relation to find the components of the velocity:

    Vx = 40m/s*cos(30°) = 34.64m/s

    Vy = 20m/s.

    First step:

    We want to find the time needed to the stream to hit the buildin.

    The horizontal speed is 34.64m/s and the distance to the wall is 50m

    So we want that:

    34.64m/s*t = 50m

    t = 50m/(34.64m/s) = 1.44 seconds.

    Now we need to calculate the height of the stream at t = 1.44s

    Second step:

    The only force acting on the water is the gravitational one, so the acceleration of the stream is:

    a(t) = -g.

    g = -9.8m/s^2

    For the speed, we integrate over time and we get:

    v(t) = -g*t + v0

    where v0 is the initial speed: v0 = 20m/s.

    The velocity equation is:

    v(t) = -g*t + 20m/s.

    For the position, we integrate again over time:

    p(t) = -(1/2)*g*t^2 + 20m/s*t + p0

    p0 is the initial height of the stream, this data is not known.

    Now, the height at the time t = 1.44s is

    p(1.44s) = -5.9m/s^2*(1.44s)^2 + 20m/s*1.44s + po

                 = 16.57m + p0

    So the height at wich the stream hits the building is 16.57 meters above the initial height of the fire hose.

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