Free Fall Equation (Air Drag) (Q3836): Difference between revisions

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Changed claim: defining formula (P29): \begin{align} m\dot{v}&=mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right)\\ \end{align}
Changed claim: defining formula (P29): \begin{align} m\dot{v}&=mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right)\\ v(t) &= v_{\infty}\tanh\left(\frac{gt}{v_{\infty}}\right) \end{align}
Property / defining formulaProperty / defining formula

mv˙=mg12ρCDAv2y(t)=y0+v0tv2glncosh(gtv)

\begin{align} m\dot{v}&=mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right)\\ \end{align}

mv˙=mg12ρCDAv2y(t)=y0+v0tv2glncosh(gtv)v(t)=vtanh(gtv)

\begin{align} m\dot{v}&=mg-\frac{1}{2}\rho C_DAv^2 \\ y(t)&=y_0+v_0t-\frac{v_\infty^2}{g}\ln\cosh\left(\frac{gt}{v_\infty}\right)\\ v(t) &= v_{\infty}\tanh\left(\frac{gt}{v_{\infty}}\right) \end{align}

Revision as of 10:11, 10 October 2024

Modeling the fall of objects by the laws of classical mechanics, including the aerodynamic drag and assuming a uniform gravitational field. Moreover, assuming the falling object to be a point mass.
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Free Fall Equation (Air Drag)
Modeling the fall of objects by the laws of classical mechanics, including the aerodynamic drag and assuming a uniform gravitational field. Moreover, assuming the falling object to be a point mass.

    Statements

    Q3832 (Deleted Item)
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    mv˙=mg12ρCDAv2y(t)=y0+v0tv2glncosh(gtv)v(t)=vtanh(gtv)
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    P853 (Deleted Property)
    The value is invalid and cannot be displayed. Property P853 not found, cannot determine the data type to use.
    P891 (Deleted Property)
    The value is invalid and cannot be displayed. Property P891 not found, cannot determine the data type to use.
    The value is invalid and cannot be displayed. Property P891 not found, cannot determine the data type to use.
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