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## Work

Work transfers energy to a system through the forceful manipulation of its state. Do some work on yourself to master this fundamental mode of energy transfer.

# Rocket Physics

A rocket's engine ejects fuel at a rate of $$40 \text{ kg/s}$$ with an exhaust velocity of $$4000 \text{ m/s}.$$ If the rocket's initial mass is $$24000 \text{ kg},$$ what is the approximate change in velocity after $$24$$ seconds?

A rocket whose mass is $$M_i = 2600 \text{ kg},$$ of which $$2080 \text{ kg}$$ is fuel, consumes fuel at a rate of $$R = 26 \text{ kg/s}.$$ The exhaust velocity of the fuel relative to the rocket engine is $$v_e = 400 \text{ m/s}.$$ If the fuel consumption rate is changed to double the thrust, how long can the rocket fire the engine?

A $$5000 \text{ kg}$$ space shuttle moving toward Moon with velocity $$100 \text{ m/s}$$ fires its rocket engine. The rocket engine ejects exhaust at a speed of $$300 \text{ m/s}$$ relative to engine. If the final speed of the shuttle is $$130 \text{ m/s},$$ what is the approximate amount of exhaust the shuttle has ejected?

A rocket of mass $$5000 \text{ kg}$$ ejects fuel at a rate of $$R = 5 \text{ kg/s}$$ with an exhaust velocity of $$v_e = 3000 \text{ m/s}.$$ If the rocket's initial velocity is $$v_i = 1800 \text{ m/s},$$ approximately how long will it take to reach a velocity of $$v_f =2700 \text{ m/s}?$$

A rocket whose initial mass is $$M_i = 1380 \text{ kg}$$ consumes fuel at rate of $$R = 22 \text{ kg/s}.$$ The exhaust velocity of fuel relative to the rocket engine is $$v_e = 200 \text{ m/s}.$$ Find the thrust that the rocket engine provides.

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