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Matt_993
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Homework Statement
At time t=0 a dust particle of mass m_0 starts to fall from rest through a cloud. Its mass grows exponentially with the distance fallen, so that after falling through a distance x its mass is m_0exp[αx] where α is constant. Show that at time t the velocity of the particle is given by:
v=sqrt(g/α)tanh(t(sqrt(αg))
Homework Equations
Variable mass equation:
mg= mv'+vm'
The Attempt at a Solution
Using the variable mass equation I've fiddled around with it and gotten out a differential equation in terms of v, which is:
dv/dt=-αv^2+g
Which after filling in the answer I am looking for is the correct equation. However solving it properly by hand seems harder as its a non-linear ODE. I was just wondering is there any other way of going about this problem or if not, can anyone give me a tip on how to solve the ODE properly.
Thank you for your time
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