Calculating Rocket Height with Changing Mass: Guide & Tips

AI Thread Summary
To calculate the height reached by a rocket with changing mass, one must consider the specific impulse, mass ratio, and thrust-to-weight ratio. Key equations include the Tsiolkovsky rocket equation, which relates the change in velocity to the mass ratio and specific impulse. Understanding the thrust-to-weight ratio is crucial for determining the acceleration and subsequent height. Participants in the discussion suggest collaborating with study groups for problem-solving. Ultimately, grasping these principles is essential for accurate calculations in rocketry.
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How do you go about finding the height reached by a rocket with a changing rocket mass if you know the specific impulse, the mass ratio (original mass/final mass) and the thrust to weight ratio? Any help you can give is greatly appreciated.

edit: I would show you my work on this problem but the honest truth is I do not know where to begin.
 
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Good places to start:

What equations do you have that you think *might* apply?
 
nevermind I went to a study group and we figured it out *hopefully*
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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