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I need to compute the time of flight of a projectile which is subject to air resistance.

Here's where I am so far in solving the problem:

[tex]F_{drag} = -B v^2[/tex]

[tex]a = \frac{\partial v}{\partial t} = \frac{-B v^2}{m}[/tex]

integrate and solve for v...

[tex]v = \sqrt[3]{\dfrac{1}{3 \dfrac{B}{m} t + C}}[/tex]

I then plug this into the kinematics equation for position:

[tex]y = \frac{1}{2} a t^2 + v_0 t[/tex] ([tex]y_0[/tex] is taken to be 0)

[tex]y = \frac{1}{2} (g - \frac{F_{drag}}{m}) t^2 + v_0 t[/tex]

Substitute the equation for v into [tex]F_{drag}[/tex], which is substituted into the above equation. Next, I set y = 0 and try to solve for t... but the equation is too messy and I can't manage to get just the t's onto one side of the equation.

Am I on the right track? Is there a better way?

Thanks!

Here's where I am so far in solving the problem:

[tex]F_{drag} = -B v^2[/tex]

[tex]a = \frac{\partial v}{\partial t} = \frac{-B v^2}{m}[/tex]

integrate and solve for v...

[tex]v = \sqrt[3]{\dfrac{1}{3 \dfrac{B}{m} t + C}}[/tex]

I then plug this into the kinematics equation for position:

[tex]y = \frac{1}{2} a t^2 + v_0 t[/tex] ([tex]y_0[/tex] is taken to be 0)

[tex]y = \frac{1}{2} (g - \frac{F_{drag}}{m}) t^2 + v_0 t[/tex]

Substitute the equation for v into [tex]F_{drag}[/tex], which is substituted into the above equation. Next, I set y = 0 and try to solve for t... but the equation is too messy and I can't manage to get just the t's onto one side of the equation.

Am I on the right track? Is there a better way?

Thanks!

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