Question:

Problems dealing with motion

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a plane is flying horizontally at 8.0m/s. when a box is horizontally backward with a speed of 12m/s relative to the plane. ignoring air resistance, what is the horizontal distance between the package and the helicopter when the package hits the ground?

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  1. I don't think you will get any "numerical" answer to this problem of yours for the very simple reason that you have incomplete data given in relation to what you need determined.

    At the very least, the altitude of the plane could have been given and this will make your problem solvable.

    Anyway, to solve this problem, the first step is to determine the time it will take the box to hit the ground.

    Let us call this time "T" ...

    To do this, use the formula,

    Y = Vy(T) + (1/2)gT^2

    where

    Y = altitude of the airplane

    Vy = vertical component of the velocity of the box = 0

    g = acceleration due to gravity = 9.8 m/sec^2 (constant)

    T = time for box to hit the ground

    Since Vy = 0, then the above becomes

    Y = (1/2)gT^2

    From this equation, it is now clear why the altitude of the airplane needs to be one of the given data.

    Let

    D = horizontal distance between the package and the helicopter when the package hits the ground

    Then,

    D = (8 + 12)T = 20T

    The above is the procedural solution to your problem. Again, should the altitude of the plane be given, then both "T" and "D" can be easily determined.

    Hope this helps.


  2. You have not given the height at which the plane is flying and the box supposedly flying backward and falling freely to the ground from the same height.

    In the absence of the information, the answer to your question is not possible.

    If the height is given, you can find the point at which the box will hit the ground and the point at which the plane will reach after the time taken by the box to hit the ground.

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