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Finding differential equation of motion

The problem is in the attachment.


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I'm going to assume that you've done some work with rocket propulsion in the absence of external forces - i.e. rockets in space. In that case, the following facts should be review:

1) Thrust force on a rocket due to the ejection of fuel as it burns is given by:
Thrust = -V dM/dt
Where V is the speed of the ejected fuel relative to the rocket, and dM/dt is the rate of change of the mass of the rocket due to fuel burning. (The negative sign just indicates that the force on the rocket is in the opposite direction to the motion of the fuel as it's ejected).

2) In free space, you would use ...

Solution Summary

The solutions reviews thrust force on a rocket, conservation of momentum and external force in 488 words. Explanations and equations are used to solve the problem.