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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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