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Math Help - free fall story problem

  1. #1
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    free fall story problem

    A rescue package is being dropped out of a helicopter to a stranded group 400 ft below with an approximate angle of depression of 75 degrees. The falling object is at 337.94 ft 2 seconds after leaving the helicopter. It hits the ground at 5.0304 seconds. Create a function that models the height of the package over time.
    What type of function would I use for this problem?
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  2. #2
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    Quote Originally Posted by Chica513 View Post
    A rescue package is being dropped out of a helicopter to a stranded group 400 ft below with an approximate angle of depression of 75 degrees. The falling object is at 337.94 ft 2 seconds after leaving the helicopter. It hits the ground at 5.0304 seconds. Create a function that models the height of the package over time.
    What type of function would I use for this problem?
    I can't see how this is a "free-fall" problem as the acceleration of the object is not g. Here's how I would approach this.
    We can assume that the acceleration is constant, so we can model the height as
    h(t) = h_0 + v_0t - (1/2)at^2

    We can typically take h0 to be the height at ground level, so set h0 = 0 ft. Then we have
    h(t) = v_0t - (1/2)at^2

    You know that
    h(2) = 337.94 = v_0(2) - (1/2)a(2^2)

    and
    h(5.0304) = 0 = v_0(5.0304) - (1/2)a(5.0304^2)

    We have two simultaneous equations in v0 and a.

    -Dan
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