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21 February, 13:43

An American Red Cross plane needs to drop emergency supplies to victims of a hurricane in a remote part of the world. The plane is traveling horizontally at 100.0 m/s at a height of 50.0 m above the ground. What horizontal distance does the package travel before striking the ground?

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  1. 21 February, 14:08
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    Refer to the diagram shown below.

    Assume that air resistance is ignored.

    Note:

    The distance, h, of a falling object with initial vertical velocity of zero at time t is

    h = (1/2) gt²

    where

    g = 9.8 m/s²

    The initial vertical velocity of the supplies is 0 m/s.

    It the time taken for the supplies to reach the ground is t, then

    (50 m) = (1/2) * (9.8 m/s²) * (t s) ²

    Hence obtain

    t² = 50/4.9 = 10.2041

    t = 3.1944 s

    The horizontal distance traveled at a speed of 100 m/s is

    d = (100 m/s) * (3.1944 s) = 319.44 m

    Answer: 319.4 m (nearest tenth)
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