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Limits and Free Falling Objects

  1. Sep 28, 2008 #1
    Use the position function s(t)=-49t^(2) + 200 which gives the height of an object that has fallen from a height of 200 meters. The velocity at time t = a seconds is given by the limit as t goes to a = (s(a) - s(t))/(a-t).
    At what velocity will the object impact the ground?

    I used V^2 = 2gh and got 62.6 m/s, but am not sure if that is right or if there is another formula I should use.
  2. jcsd
  3. Sep 28, 2008 #2


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    The question asks you to find [itex]v(a)[/itex] by computing the limit,

    [tex]\lim_{t \to a} \frac{s(a)-s(t)}{a-t}[/tex]

    not by plugging it into a kinematics formula.

    [itex]v(a)[/itex] is the instantaneous speed of the object at the time [itex]t=a[/itex]. The V you just found is different; it is the speed of the object the instant before it hits the ground, not the speed at t=a. Try your hand at the limit above.
    Last edited: Sep 28, 2008
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