- #1
RenaltJ
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Homework Statement
A particle of mass "m" whose motion start with downard velocity V0 in a constant gravitational field. The drag force is quadratic and proportional to kmv2. What is the distance s through which the particle falls in accelerating from v0 to v1. Give your expression for s in terms of k, g, v0, v1
Homework Equations
F = m[itex]\frac{dv}{dt}[/itex]=mg - kmv2
The Attempt at a Solution
My attempt:
[STRIKE]m[/STRIKE](g-kv2) = [STRIKE]m[/STRIKE][itex]\frac{dv}{dt}[/itex]
ergo:
[itex]\frac{dv}{dt}[/itex] = (g-kv2)
Separating:
[itex]\int[/itex]dv/(kv2-g) = [itex]\int-kdt[/itex]
Yields:
√k/√g*arctan(√k*V/√g) = -kt + C
Pretty much stuck at this point, and am not even sure this is the proper way.