A toy rocket is launched from the ground straight upward. The height of the rocket above the ground, in feet, is given by the equation ℎ() =

Question

A toy rocket is launched from the ground straight upward. The height of the rocket above the ground, in feet, is given by the equation ℎ() = −162 + 64, where is the time in seconds. Determine the domain, using interval notation, for this function in the given context.

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Reagan 2 weeks 2021-09-11T19:00:52+00:00 1 Answer 0

Answers ( )

    0
    2021-09-11T19:02:38+00:00

    Answer:

    Although strictly speaking of mathematics i.e. theoritically,  

    t

    can take any value from  

    {


    ,

    ]
    ,

    however, it is essentially a physical problem related to Physics and we cannot have negative  

    t  i.e.  t

    0

    Further, after the maximum is reached at  t
    =
    2  (observe that first differential is  h

    (
    t
    )
    =

    32
    t
    +
    64
    , which is zero at  t
    =
    2  and second derivative  h


    (
    t
    )
    =

    32  is negative and at this we have  h
    (
    2
    )
    =
    64
    ), at  t
    =
    4
    ,  h
    (
    4
    )
    =
    0  i.e. toy rocket falls back to the ground and as such, we cannot have  h
    >
    4
    .

    Hence, domain for  t  is  [
    0
    ,
    4
    ]
    .

    tbh google

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