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Equation Thrust - Momentum Transfer Consider a vehicle made up of mass m m moving at velocity v at time t. At time t t mass m has been ejected from the vehicle with a relative velocity v 2 so that m has a velocity v v 2 . The velocity of mass m is v v t m M v v t t m m v v2 The momentum of the system at time t is m mv The momentum of the system at time t t mv v m v v2 Since momentum is conserved for this isolated system we have m v v m v v2 m m v can We rewrite this as mv v m v v2 m mv 0 Expanding mv m v mv mv 2 mv mv 0 Simplifying m v mv 2 0 v m This can be written m v2 0 t t since this happened in a time t . Taking the limit as t becomes infinitesimally small dv dm m v2 0 dt dt dv dm Rewriting m v2 dt dt dm m Denoting dt as the mass rate of flow leaving the vehicle of mass m we can write dv m m v2 dt This ejection of mass looks like a force acting on the vehicle of mass m. We call this the FT m v 2 thrust:

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