- #1
Celso
- 33
- 1
- Homework Statement
- Show that the terminal speed of a falling spherical object is given by ##v_{t} = [ (mg/c_{2})+(c_{1}/2c_{2})^2]^{1/2} - (c_{1}/2c_{2})## when both the linear and the quadratic terms in the drag force are taken into account.
- Relevant Equations
- ##m\ddot x = c_{2}v^2 + c_{1}v - mg##
To write ##v## as a function of time, I wrote the equation ##m\frac{dv}{dt} = c_{2}v^2 + c_{1}v - mg \implies \frac{mdv}{c_{2}v^2 + c_{1}v - mg} = dt##
To solve this, I thought about partial fractions, but several factors of ##-c_{1} \pm \sqrt {c_{1}^2 +4c_{2}*mg}## would appear and they don't show up in the resolution of the problem statement
To solve this, I thought about partial fractions, but several factors of ##-c_{1} \pm \sqrt {c_{1}^2 +4c_{2}*mg}## would appear and they don't show up in the resolution of the problem statement
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