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Free fall problem involving two objects

  1. Jul 26, 2010 #1
    1. The problem statement, all variables and given/known data
    A stone is thrown vertically into the air from a tower 110 ft. high at the same time that a second stone is thrown upward from the ground. The initial velocity of the first stone is 60 ft/s and that of the second stone 85 ft/s. When and where will the stones be at the same height from the ground?

    *note* When I asked my teacher, he said the "thrown vertically" meant that the stone was thrown upward


    2. Relevant equations
    Vf = Vi+gt
    d=Vit-0.5gt2


    3. The attempt at a solution

    I have two solutions. One by me and the other from my classmate. According to the teacher, her solution is correct, but I disagree.

    *Solution of classmate*

    Conversion of units:

    110ft = 33.53m
    60ft/s = 18.29m/s
    85ft/s = 25.91m/s

    d1+33.53m=d2
    18.29t - 4.9t2 + 33.53 = 25.91t - 4.9t2
    33.53 = 25/91t - 18.29t
    t = 4.4s
    18.29 (4.4) - 4.9 (4.4)2 + 33.53 = 19.13m

    *My solution* - I believe that my classmate failed to take into account the first stone being thrown upwards. However, there is also something wrong with my solution.

    Conversion of units:

    110ft = 33.53m
    60ft/s = 18.29m/s
    85ft/s = 25.91m/s

    18.29 = 9.8t
    1.87 = t
    18.29(1.87) - 0.5(9.8)(1.87)2 + 33.53 = d of stone 1 at 1.87s from the ground
    d = 50.6m

    25.91 = 9.8t
    2.64 = t
    25.91(2.64) - 0.5(9.8)(2.64)2 = d of stone 2 at 2.64s from the ground
    d = 34.25

    2.64 - 1.87 = 0.77s
    9.8(0.77) = V
    d = 2.91m
    50.6 - 2.91 = 47.69m = d of stone 1 at 2.64s from the ground

    47.69 - (7.55t + 0.5(9.8)t2) = 34.25 - (0.5(9.8)t2
    13.44 = 7.55t
    t = 1.78s
    Plugging in t to the formula for t, d = 28.96m
    47.69 - 28.96 = 18.73 m
    1.78 + 2.64 = 4.42s

    Therefore, my answer is 4.42 s at 18.73 m from the ground
     
  2. jcsd
  3. Jul 26, 2010 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The solution of your classmate is correct. Your piecewise solution might be correct, but unnecessarily complicated with a lot of rounding errors. That can be the reason of the different results.

    ehild
     
  4. Jul 27, 2010 #3
    I see. Thank you very much :)
     
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