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[Mechanics] Solving equations with 2 variables

  1. Nov 8, 2008 #1
    Hello there, I am having a lot of trouble solving a question with which I cannot even begin, I have tried making 2 equations and equation, but I just end up with some number = 0, which is of course wrong, here is the question.


    A stone is dropped from the top of a tower. One second later another stone is thrown vertically downwards from the same point with a velocity of 14ms^-1. If they hit the ground together find the height of the tower.

    I've managed to get that..

    First rock

    s = ?
    u = 0
    v = ?
    a = 9.8
    t = ?

    Second rock

    s = ?
    u = 14
    v = ?
    a = 9.8
    t = ?

    Now where do I go from here? I've tried making 2 equations using the same base equation i.e. v^2 = u^2 + 2as with the different values and then equating them, which doesn't work.

    Any help would be much appreciated, thanks.
  2. jcsd
  3. Nov 8, 2008 #2


    User Avatar
    Science Advisor

    You haven't really shown much. Where did you get the formula v^2+ u^2+ 2as? "Conservation of energy".

    I would just use the dynamics equations: If an object falls under gravity with initial velocity v, then s= -4.9t2+ vt is the distance it has fallen. The first rock has fallen, at time t, a distance h= -4.9t2 and the second rock has has fallen a distance h= -4.9(t-1)2- 14(t-1). Those are negative because it is downward. The second equation has t-1 because the rock was thrown one second after the first rock so the time it has been falling is 1 less. Since the height, h, and the time, t, are the same for those two rocks, you can solve the two equations for h and t. h is what you are asked.
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