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Two objects - when do they meet?

  1. Oct 24, 2007 #1
    1. The problem statement, all variables and given/known data
    An object is thrown downward with an initial
    speed of 4 m/s from a height of 99 m above the
    ground. At the same instant, a second object
    is propelled vertically from ground level with
    a speed of 25 m/s.

    The acceleration of gravity is 9.8 m/s^2.

    At what height above the ground will the
    two objects pass each other? Answer in units
    of m.

    2. Relevant equations
    None - I believe you make your own equation.
    Look below to see what I mean.

    3. The attempt at a solution
    Well I tried to find the position equation of both
    objects, then set them equal to each other to
    find the time at which their positions are equal.

    For the top object, since at time 0 his position
    is 99 m, and his initial velocity is 4 m/s, I found
    its position equation to be x(t) = -4t + 99. The
    -4t is negative because its traveling down.

    For the bottom object, since at the time 0 his
    position is also 0, it has no constant. His initial
    velocity is 25 m/s, so I got his position equation
    to be x(t) = 25t. The 25 t is positive because he
    is propelled upwards.

    So I set the two equations equal, and solved for t:

    -4t + 99 = 25t
    99 = 29t
    t = 3.4138

    I plugged this time into one of my position
    equations to find the position when they
    x(t) = 25t
    x(3.4138) = 25(3.4138)
    x = 85.3448 m

    This answer seemed to make sense, because
    since the bottom object is propelled significantly
    faster than the top object, they should meet
    somewhere close to the 99 m mark.

    But low and behold, 85.3448 m is incorrect.

  2. jcsd
  3. Oct 24, 2007 #2


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    Science Advisor
    Homework Helper

    You quoted a figure for the acceleration of gravity but your equations are all assuming constant velocity. Put g into the problem.
  4. Oct 24, 2007 #3
    Don't forget, your "top" and "bottom" objects won't stay at [itex]4ms^{-1}[/itex] & [itex]25ms^{-1}[/itex] forever, they experience gravity. I suggest you look at this equation for a free-fall object:

    [tex]x(t) = x_0 + ut - \frac{1}{2}gt^2[/tex] See if you can apply this to the problem
  5. Oct 24, 2007 #4
    Do you think I'm giving too much help :confused:
  6. Oct 24, 2007 #5


    User Avatar
    Science Advisor
    Homework Helper

    Solving the problem for them is too much. Beyond that, how explicit with hints you want to be is completely up to you.
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