Solve Rocket Propulsion Problem: a = ((Vr)(k))/(1-(kt))-g

[mopar969]

Here is what I know a = (-Vr/m)(dm/dt)-g, I also know that 6. : m=m(initial)(1-kt). Under the conditions of 6: Show that a = ((Vr)(k))/(1-(kt))-g. I have tried to solve this problem by substituting dm/dt=-km(initial) into the first equation I have listed (a = etc.) but I have had no luck. Please help me solve this problem!

 

[Delphi51]

Subbing DM/dt = -Mi*k into a = - Vr/M*dM/dt - g
I get a = (-Vr)(-Mi*k)/M - g = k*Vr*Mi/M - g
To get the desired expression, we must eliminate the M's.
From the original expression for m, rearranged, we have
Mi/M= 1/(1-kt)
Putting this into line 2 above, we have a = k*Vr/(1-kt) - g