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Homework Statement
vertical rocket start:
F_thrust (simple F)
Δm (fuel consumed per Δt)
m_tot
the relative velocity of the gas w is demanded.
Homework Equations
vgas=v+Δv+w, w<0
m(t)=mtot-Δm*t
The Attempt at a Solution
rocket acceleration.
F-G=m(t)*a(t)
a(t)=F/m(t)-g
first:
v*m=Δm*vgas+(v+Δv(t))(m-Δm)
⇒w=-Δv(t)*m(t)/Δm
Δv(t)=a(t)*Δt
or second direct way:
w=F/Δm*Δt
so the first one should lead to the direct solution if I'm not mistaken, but I struggle to get the correct solution.
To be more specific, it seems in order to get the same result Δv=(a+g)Δt but this wouldn't make much sense for me.
thanks in advance
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