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Why the answer in book does not match the clue given

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  1. May 14, 2017 #1
    1. The problem statement, all variables and given/known data

    An elevator ascends from the ground with uniform speed. At time ##T_1## a boy drops a marble through the floor. The marble falls with uniform acceleration ##9.8## m/s^2 and hits the ground ##T_2## seconds later. Fiind the height of the elevator at time ##T_1##. Clue : if ##T_1 = T_2 = 4## then ##h = 39.2m ##.


    2. Relevant equations


    3. The attempt at a solution
    I let the uniform speed be ##u##,

    The displacement is ##-h## in time ##T_2##.

    ##-h = uT_2 - \dfrac{1}{2}g T_2^2##

    Also
    And ##u = \dfrac{h}{T_1}##

    So, ##-h = \dfrac{hT_2}{T_1} - \dfrac{1}{2}gT_2^2##

    Combining them I get

    ##h = \dfrac{ g T_2^2 T_1}{2(T_2 + T_1) }##

    Is the correct ?

    But the given answer is ##h = \dfrac{T_1}{T_2}\dfrac12g(T_1 - T_2)^2 ##

    Also there answer does not match the given clue ? is the given answer wrong ?
     
  2. jcsd
  3. May 14, 2017 #2

    TSny

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    Homework Helper
    Gold Member

    Looks like your answer is correct.

    Their answer appears to correspond to having ##T_2## be the total time since ##T = 0## rather than the time since ##T_1##. But, that's not the correct meaning of ##T_2## according to the statement of the question.
     
  4. May 14, 2017 #3
    I guess the solution manual was not created by the original authors.
     
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