Rocket physics equation problem

[mopar969]

Suppose the rate of ejection mass by a rocket is a constant, dm/dt = -kmo. I need to show that m=mo(1-kt). I know -mg=m(dv/dt)-Vr(dm/dt). I thought that I could just substitute for (dm/dt) and get the solution but I am having no luck. Please help me show this property.

 

[kreil]

You need to integrate the equation given to you for the mass loss

$$\frac{dm}{dt} = -k m_0 \implies \int_{m_0}^{m(t)}dm = - k m_0 \int_0^t dt'$$

 

[mopar969]

My question is how does this relate to the equation that I posted? aka: -mg=m(dv/dt)-Vr(dm/dt)

 

[mopar969]

Do I have the right equation?