Energy Budget for a Rocket in Free Space: Recall the analysis of the rocket engine in Project I, Flight of the Rocket. Although the momentum of the rocket and its exhaust is conserved (constant), their energy is not; energy must be supplied by the combustion of fuel. WARNING: This is not the same as the energy requirement of the jet airplane in Project II, Nonstop Service to Anywhere. Using the same approach we used to derive the First and Second Rocket Equation ---- sequential “snapshots” of the rocket---obtain an expression for the total kinetic energy gained by rocket and exhaust during the engine burn, in terms of the initial and final rocket masses Mi and Mf , the nozzle speed U of the exhaust, etc. This is the energy that must be supplied by combustion. HINTS: You may need to use the First Rocket Equation in your calculation. You may also use the fact that squares and products of differentials are negligible compared to the differentials themselves.

Question

Energy Budget for a Rocket in Free Space: Recall the analysis of the rocket engine in Project I, Flight of the Rocket. Although the momentum of the rocket and its exhaust is conserved (constant), their energy is not; energy must be supplied by the combustion of fuel. WARNING: This is not the same as the energy requirement of the jet airplane in Project II, Nonstop Service to Anywhere. Using the same approach we used to derive the First and Second Rocket Equation ---- sequential “snapshots” of the    rocket---obtain an expression for the total kinetic energy gained by rocket and exhaust during the engine burn, in terms of the initial and final rocket masses Mi and Mf , the nozzle speed U of the exhaust, etc. This is the energy that must be supplied by combustion. HINTS: You may need to use the First Rocket Equation in your calculation. You may also use the fact that squares and products of differentials are negligible compared to the differentials themselves.