College math

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A rock is thrown from the top of a tower that is 400 feet tall. If its height above the ground can be modeled by

h = -16t2 + 64t +400 where h is in feet, and t is in seconds.
To the nearest tenth of a second, how long does it take the rock to reach the ground?
To the nearest tenth of a second, how long will it take the rock to reach its maximum height?

To the nearest tenth of a foot, how high will the rock go before it starts falling down?

  • College math -

    Hf=0=400+64t-16t^2

    use the quadratic equation
    a=-16, b=64, c=400

    Now how high? Lets do some Gedunken.

    if we find the time it takes for the rock to leave the tower, and return to the same altitute it started from
    400=400+64t-16t^2 or
    0=t(64-16t) the solutions are t=0, and t=4 seconds. Now the rock is at maximkum height in half that, or at t=2seconds
    h=400+64t-16t^2 solve for t=2

  • College math -

    I would like to point out a basic misunderstanding your teacher has with falling down. The rock is falling the instant is thrown upwards, that is why is slows down until the max height.

    Satellites in earth orbit, albeit at constant altitude, are constantly falling, otherwise, they would go off in space.

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