The query seems incomplete, but based on the information provided, here is an analysis related to a space launch vehicle with a mass of 100,000 kg at liftoff achieving a velocity of 700 m/s. To understand the energy involved:
- The kinetic energy EkE_kEk of the vehicle at velocity vvv is given by:
Ek=12mv2E_k=\frac{1}{2}mv^2Ek=21mv2
where m=100,000 kgm=100,000\text{ kg}m=100,000 kg and v=700 m/sv=700\text{ m/s}v=700 m/s.
Calculating:
Ek=12×100,000×(700)2=0.5×100,000×490,000=24,500,000,000 J=24.5 GJE_k=\frac{1}{2}\times 100,000\times (700)^2=0.5\times 100,000\times 490,000=24,500,000,000\text{ J}=24.5\text{ GJ}Ek=21×100,000×(700)2=0.5×100,000×490,000=24,500,000,000 J=24.5 GJ
So, the vehicle has 24.5 gigajoules of kinetic energy at 700 m/s. Regarding the power output or energy required at liftoff:
- Rocket engines produce enormous power; for example, a Falcon 9 rocket produces about 26 GW of power at liftoff, burning fuel at a rate of hundreds of kilograms per second and converting chemical energy into kinetic energy and heat with about one-third efficiency in thrust generation
- The overall efficiency of rockets in converting chemical energy of fuel into kinetic energy of payload is low, often around 6% when considering total propellant energy vs payload kinetic and potential energy
- The mass loss during launch (fuel consumption) affects exhaust velocity and thrust but is accounted for in rocket propulsion equations and trajectory optimization
In summary, a 100,000 kg rocket reaching 700 m/s has about 24.5 GJ of kinetic energy, and achieving this requires burning large amounts of fuel with high power output engines, with typical rocket liftoff power in the tens of gigawatts range
