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I'm at a loss trying to figure out the specific force that pushes a missile at rest off the ground, to the high sky.

Considering a missile with constant mass, and an independent initial total fuel mass. The rate of fuel mass being expelled out of the missile is constant, in (kg/s); the fuel gas exits the missile at a constant speed wrt to the missile, in (m/s).

For convenience, I'm considering a 1-D case, along the height axis only.

My question is, the calculation of the force that points upward, pushing the missile through the air, with regard to the extent of Newtonian mechanics only.

I have tried applying Lagrangian mechanics to find the force, using the Lagrange-Euler equation for the case with external force, but the result did not seem consistent.

Please, help me if you have the time!

Thanks in advance!

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# I The physics of a missile with uniform rate of fuel loss

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