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Thread: antiderivative world problem

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    antiderivative world problem

    A stone is dropped from the top of a 450 m tower. (Acceleration due to gravity is -9.8 m/s2. Ignore air resistance. Give your answers correct to two decimal places.)

    (a) Find the distance of the stone above ground level at time t.
    $\displaystyle s(t)=$$\displaystyle 450 - \frac{9.81t^2}{2}$

    (b) How long does it take the stone to reach the ground?

    $\displaystyle 0 = 450 - \frac{9.81t^2}{2}$

    $\displaystyle t = \sqrt\frac{(2 * 450)}{ 9.81} $
    =$\displaystyle 9.58 sec.$

    (c) With what speed does it strike the ground? This is the part I keep getting wrong.

    $\displaystyle
    v(t)=-9.8t$
    =$\displaystyle -9.8(9.58)$
    =$\displaystyle -93.97$
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    Quote Originally Posted by hazecraze View Post
    A stone is dropped from the top of a 450 m tower. (Acceleration due to gravity is -9.8 m/s2. Ignore air resistance. Give your answers correct to two decimal places.)

    (a) Find the distance of the stone above ground level at time t.
    $\displaystyle s(t)=$$\displaystyle 450 - \frac{9.81t^2}{2}$

    (b) How long does it take the stone to reach the ground?

    $\displaystyle 0 = 450 - \frac{9.81t^2}{2}$

    $\displaystyle t = \sqrt\frac{(2 * 450)}{ 9.81} $
    =$\displaystyle 9.58 sec.$

    (c) With what speed does it strike the ground? This is the part I keep getting wrong.

    $\displaystyle
    v(t)=-9.8t$
    =$\displaystyle -9.8(9.58)$
    =$\displaystyle -93.97$
    speed is a scalar > 0
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