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John004
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Homework Statement
A rocket with initial mass of m0. The engine that can burn gas at a rate defined by m(t)=m0-αt, and expel gas at speed (relative to the rocket) of u(t)=u0-βt. Here, m0, α, u0, and β are all constants. Assume the lift-off from ground is immediate
a) The rocket speed v(t)=?
b) The rocket height (from ground) y(t)=?
Homework Equations
F = dp/dt
The Attempt at a Solution
So F = dp/dt → -mg = u dm/dt + m dv/dt since dm/dt = -α → -g = (-α/m)u + dv/dt
→ ∫(-g + α(u0 - βt)/(m0 - αt) dt) = v
so I am not really too sure about how to solve the above integral