- #1
coolusername
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Homework Statement
A 20 kg rock falls with the force of gravity acting on it. Another force acts on the rock (same direction as gravity) that is proportional to the velocity squared, 100v^2. Come up with an expression of the rock's velocity at any time t.
Homework Equations
Hint: (d/dx)(tan^-1(x)) = 1/(1 + x^2)
The Attempt at a Solution
F(net) = ma = Fg + 100v^2
ma = mg + 100v^2
a = g +(100v^2)/m (m=20)
dv/dt = g + 5v^2
dv/dt = g((5/g)v^2 + 1)
dv/((5/g)v^2 + 1) = g(dt)
dv/((root(5/g)*v)^2 +1) = g(dt) (integrate both sides)
tan^-1(root(5/g)*v) = gt + C
root(5/g)*v = tan(gt + C)
v(t) = (root(g/5))tan(gt + C)
I want to know if I can get rid of the constant as well as if my approach to the general solution is correct. Also if my general soln is correct.
Thanks!