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Math Help - Transformation of functions and their graphs

  1. #1
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    Transformation of functions and their graphs

    A ballet dancer jumps in the air. The height, h(t), in feet, of the dancer at time t, in seconds since the start of the jump, is given by ^4.

    h(t) = -16t^2 + 16Tt

    where T is the total time in seconds that the ballet dancer is in the air.

    Show that the time, T, that the dancer is in the air is related to H, the maximum height of the jump by the equation:

    H = 4T^2

    Thanks a whole bunch!
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  2. #2
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    Hello hydride
    Quote Originally Posted by hydride View Post
    A ballet dancer jumps in the air. The height, h(t), in feet, of the dancer at time t, in seconds since the start of the jump, is given by ^4.

    h(t) = -16t^2 + 16Tt

    where T is the total time in seconds that the ballet dancer is in the air.

    Show that the time, T, that the dancer is in the air is related to H, the maximum height of the jump by the equation:

    H = 4T^2

    Thanks a whole bunch!
    The velocity of the dancer at time t is given by

    v = h'(t) = -32t+16T

    The dancer is at the maximum height when v=0; i.e. when t = \tfrac12T

    So the maximum height H is given by H=h(\tfrac12T)=-16(\tfrac12T)^2+8T^2

    \Rightarrow H = 4T^2

    Grandad
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