- #1
DivGradCurl
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A ball with mass [tex]0.15\mbox{ kg}[/tex] is thrown upward with initial velocity [tex]20\mbox{ m/s}[/tex] from the roof of a building [tex]30 \mbox{ m}[/tex] high. There is a force due to air resistance of [tex]\frac{v^2}{1325}[/tex], where the velocity [tex]v[/tex] is measured in [tex]\mbox{ m/s}[/tex].
I've deliberately disregarded the rest of the problem. My question is about the first-order differential equation I set up based upon the given information.
[tex]m\frac{dv}{dt}=-mg-\frac{v^2}{1325}, \qquad v(0)=v_0 \quad x(0)=x_0[/tex]
[tex]\frac{dv}{dt} + \frac{v^2}{1325m} = -g[/tex]
As far as I can see, the method of integrating factors does not work here. I don't know what to do. It is possible that I made a mistake in the D.E. set up.
Any help is highly appreciated.
I've deliberately disregarded the rest of the problem. My question is about the first-order differential equation I set up based upon the given information.
[tex]m\frac{dv}{dt}=-mg-\frac{v^2}{1325}, \qquad v(0)=v_0 \quad x(0)=x_0[/tex]
[tex]\frac{dv}{dt} + \frac{v^2}{1325m} = -g[/tex]
As far as I can see, the method of integrating factors does not work here. I don't know what to do. It is possible that I made a mistake in the D.E. set up.
Any help is highly appreciated.