a plane is flying 120 m above the ground at an angle of 30 degrees to the horizontal, when the pilot released 2 fuel tanks to decrease the p

Question

a plane is flying 120 m above the ground at an angle of 30 degrees to the horizontal, when the pilot released 2 fuel tanks to decrease the planes load. How long did the tanks fall and with what speed did it hit the ground of the plane’s speed was 84 m/s?

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Orla Orla 2 weeks 2021-07-22T23:32:54+00:00 1 Answers 4 views 0

Answers ( )

    0
    2021-07-22T23:34:01+00:00

    Answer:

    • 2.26 seconds
    • 97m/s

    Explanation:

    1. Fall time

    i) Find the vertical speed of the plane when the tanks were released

             V_{y,0}=84m/s\times sin(30\º)=42m/s

    That is the same initial vertical speed of the tanks.

    ii) Find the fall time

             y-y_0=V_{y,0}\cdot t+g\cdot t^2/2

             120=42t+4.9t^2

             

             4.9t^2+42t-120=0

             

            t=\dfrac{-42\pm\sqrt{(42)^2-4(4.9)(-120)}}{2\times 4.9}

    Only the positive value has aphysical meaning: t = 2.26 seconds.

    2. Speed when they hit the ground

    i) The horizontal speed is constant:

              V_x=84m/s\times cos(30\º)\approx72.5m/s

    ii) The vertical speed is:

                V_y=V_{y,0}+g\cdot t

                V_y=42m/s+9.8m/s^2\cdot (2.26s)\approx64.1m/s

    iii) Total speed

              V=\sqrt{V_x^2+V_y^2}

              V=\sqrt{(72.5m/s)^2+(64.1m/s)^2}\approx97m/s

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )