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Math Help - Modulus (Brainteaser question)

  1. #1
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    Modulus (Brainteaser question)



    a) This I can do:







    b) My working is as follows:









    When









    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:





    When



    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
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    The equation of motion a = -\frac{v^2-900g}{900} tells you that a=0 when v = \sqrt{900g}. This is the terminal velocity v_\infty, the speed at which gravitational pull is exactly balanced by air resistance. If v < v_\infty then the acceleration will be positive, and the velocity will increase towards v_\infty. If v>v_\infty then a<0 and the velocity will decrease towards v_\infty.

    In this problem, the initial value of v is 0, so v can never exceed v_\infty. That is why you have to take 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 \sqrt{900g}, then your solution would have needed to take v^2-8820 to be positive.
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