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Thread: Modulus (Brainteaser question)

  1. #1
    Senior Member
    Apr 2009

    Modulus (Brainteaser question)

    a) This I can do:

    b) My working is as follows:


    Now how do I get rid of the mod signs to get their form? I did the following:

    But then how to get rid of the mods in the denominator? Since it still could be negative and you need the mods to ensure it's positive?

    Next part says:


    Solving these on the TI-89 gives:

    Now since the question asks for the speed we require

    However which one do you choose?

    Now if you solve their equation which is

    you get only and not

    So which formula do you use and most importantly when you use my formula how do you dismiss as a solution?
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  2. #2
    MHF Contributor
    Opalg's Avatar
    Aug 2007
    Leeds, UK
    The equation of motion $\displaystyle a = -\frac{v^2-900g}{900}$ tells you that a=0 when $\displaystyle v = \sqrt{900g}$. This is the terminal velocity $\displaystyle v_\infty$, the speed at which gravitational pull is exactly balanced by air resistance. If $\displaystyle v < v_\infty$ then the acceleration will be positive, and the velocity will increase towards $\displaystyle v_\infty$. If $\displaystyle v>v_\infty$ then a<0 and the velocity will decrease towards $\displaystyle v_\infty$.

    In this problem, the initial value of v is 0, so v can never exceed $\displaystyle v_\infty$. That is why you have to take $\displaystyle v^2-8820$ to be negative. If the problem told you that the sandbag had been hurled downwards from the balloon with an initial speed greater than $\displaystyle \sqrt{900g}$, then your solution would have needed to take $\displaystyle v^2-8820$ to be positive.
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