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Maximum velocity of object dropped from cliff

  1. Apr 10, 2013 #1
    Just finished an exam. One problem is bothering me and I want to be certain if it's right.

    1. The problem statement, all variables and given/known data
    What is the maximum velocity of an object dropped from a 20 m cliff?
    Assume no air friction and gravity is 10 m/s/s.


    2. Relevant equations
    None given, but I assume v=gt is relevant.


    3. The attempt at a solution
    15 m/s.
    My reasoning was that if after 1s, the object fell 10m at 10m/s,
    and after 2s, the object has fallen 30m (10m + 20m) at 20m/s (10m/s + 10m/s),
    then I can divide the 2nd speed increment in half to determine speed at 20m fall (10m/s + 5m/s).

    I tried using equations before answering 15.
    v=gt by itself can't work without t (t was not given).
    d=1/2gt^2 tells me the object fell for 2s, but that doesn't seem right (it would have traveled 30m).
    Assuming t=2s is right, v = 10m/s/s * 2s = 20m/s.

    So which is right: 15 or 20?
     
  2. jcsd
  3. Apr 10, 2013 #2

    PeterO

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    Homework Helper

    It's 20.
    In the first second it reaches 10m/s, but travels only 5m [average speed = (0+10)/2 = 5
    In the second second second is increases to 20 m/s, travelling a further 15m [average speed = (10+20)/2 = 15.
     
  4. Apr 10, 2013 #3
    Oh, that's right... it has to be averaged since speed isn't constant. Thanks.
     
  5. Apr 11, 2013 #4

    CWatters

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    Science Advisor
    Homework Helper

    In my day we would remember one of the the SUVAT Equations

    http://en.wikipedia.org/wiki/Equations_of_motion

    probably V2 = U2 + 2aS

    where

    V = final velocity
    U = initial velocity
    a = g ≈10
    s = displacement

    Reduces to

    V2 = 2as
    = 2 * 10 * 20
    = 400

    so V=20
     
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