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Math Help - free falling object

  1. #1
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    free falling object

    Use the position function s(t) = -16t^2 + 1000, which gives the height in feet of an object that has fallen for t seconds from a height of 1000 feet. the velocity at time t = a seconds is given by:

    lim s(a) - s(t)
    t to a a - t

    if a construction worker drops a wrench from a height of 1000 feet, how fast will the wrench be falling after 5 seconds?

    the answer is 160ft/sec
    but i am not sure how to get there,
    this is what i have so far:

    -16 * 5^2 +1000 = 600

    600 - (-16t^2 + 1000)
    5 - t

    where do i go from here? please help!
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  2. #2
    MHF Contributor Calculus26's Avatar
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    600 - (-16t^2 + 1000
    5 - t


    = (16*t^2- 400)/(5-t)

    = 16(t^2-25)/(5-t)

    = 16(t-5)(t+5)/(5-t)

    = -16(t+5)

    lim -16(t+5) =-160
    t->5

    This is the velocity hence the negative sign indicating it is moving down

    the speed is 160
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