What kind of math do I include in THIS?

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The discussion focuses on determining the appropriate type of differential equations needed to analyze a rocket's motion as it transitions from a powered phase to a projectile phase. The user is specifically interested in whether to use first-order ordinary differential equations (ODEs) due to the changing mass of the propellant over time. The problem involves conservation of momentum, particularly in the context of the rocket's propellant consumption. The user seeks guidance on understanding the relevant mathematical concepts rather than simply copying solutions. Ultimately, the key challenge lies in addressing the dynamics of the rocket while accounting for the variable mass during its powered ascent.
Ashleyz
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Here is the problem. The only help I need with this is
to determine the SPECIFIC type of defferential equations to use.
(if any at all)
i.e, 1st ODE's, ect.

A rocket starts from rest on a ramp.

Its propellant is consumed at a constant rate for a certain time.

The propellent burns out after a certain time.

Now the rocket is a projectile. It will land due to gravity at a certain D (distance) from ramp.
 
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This site is great, but I have never studied Diff. Eq. and need
to know what section I need to look at in order to solve the problem.

I need to understand, not copy and past.
 
Why not post your problem in more detail, and show us how far you've gotten and where you're stuck?
 
Read my first post.

This is a problem I am putting together(it is not homework) and need help only on
deciding if I need to include a differential equation.
If I do, then what kind? I have never taken a class on D.E's, so need help narrowing down what type.

The problem is conservation of momentum, and I am only working with variables at first.

The first part is the hard part, as the M(mass) of the P(propellent) is changing with time.
-this is the part that I believe I may need to include some ODE's.

I have made the 2nd part to this problem easy, bc the fuel runs out, and now we are dealing with an easy projectile.
 
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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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