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A 2-stage rocket is being designed to launch a space vehicle S = 500 kg. Each stage has a mass of 10Mg (that's mega-grams) and is made up of 92% fuel and 8% other components (structural components, engines, separator modules, etc.). Stage A uses high-thrust, low-efficiency engines that consume fuel at a rate of 580 kg/s and eject the exhaust at a relative velocity of 3700 m/s. Stage B uses low-thrust, high-efficiency engines that consume fuel at a rate of 180 kg/s and eject the exhaust at a relative velocity of 5700 m/s. In reality, I would start at 90° and decrease over time as the rocket ascends. However, we will consider the case where the rocket remains vertical (8 = 90°) throughout. You may also consider the engine firings as well as the jettisoning of stage A to be instant; that is, each engine fires at maximum burn from the moment they ignite, and the rocket switches to stage B at the moment stage A runs out of fuel. Using analysis for a variable system of particles, determine: (a) The speed at the moment stage A runs out of fuel (b) The speed at the moment stage B runs out of fuel (the max speed reached)

A 2-stage rocket is being designed to launch a space vehicle S = 500 kg. Each stage has a mass of 10Mg (that's mega-grams) and is made up of 92% fuel and 8% other components (structural components, engines, separator modules, etc.). Stage A uses high-thrust, low-efficiency engines that consume fuel at a rate of 580 kg/s and eject the exhaust at a relative velocity of 3700 m/s. Stage B uses low-thrust, high-efficiency engines that consume fuel at a rate of 180 kg/s and eject the exhaust at a relative velocity of 5700 m/s. In reality, I would start at 90° and decrease over time as the rocket ascends. However, we will consider the case where the rocket remains vertical (8 = 90°) throughout. You may also consider the engine firings as well as the jettisoning of stage A to be instant; that is, each engine fires at maximum burn from the moment they ignite, and the rocket switches to stage B at the moment stage A runs out of fuel. Using analysis for a variable system of particles, determine: (a) The speed at the moment stage A runs out of fuel (b) The speed at the moment stage B runs out of fuel (the max speed reached)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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A 2-stage rocket is being designed to launch a space vehicle S = 500 kg. Each stage has a mass of 10Mg (that's mega-grams) and is made up of 92% fuel and 8% other components (structural components, engines, separator modules, etc.). Stage A uses high-thrust, low-efficiency engines that consume fuel at a rate of 580 kg/s and eject the exhaust at a relative velocity of 3700 m/s. Stage B uses low-thrust, high-efficiency engines that consume fuel at a rate of 180 kg/s and eject the exhaust at a relative velocity of 5700 m/s. In reality, would start at 90° and decrease over time as the rocket ascends. However, we will consider the case where the rocket remains vertical (0 = 90°) throughout. You may also consider the engine firings as well as the jettisoning of stage A to be instant; that is, each engine fires at maximum burn from the moment they ignite, and the rocket switches to stage B at the moment stage A runs out of fuel. Using analysis for a variable system of particles, determine: (a) The speed at the moment stage A runs out of fuel (b) The speed at the moment stage B runs out of fuel (the max speed reached) 9 B S
Transcribed Image Text:A 2-stage rocket is being designed to launch a space vehicle S = 500 kg. Each stage has a mass of 10Mg (that's mega-grams) and is made up of 92% fuel and 8% other components (structural components, engines, separator modules, etc.). Stage A uses high-thrust, low-efficiency engines that consume fuel at a rate of 580 kg/s and eject the exhaust at a relative velocity of 3700 m/s. Stage B uses low-thrust, high-efficiency engines that consume fuel at a rate of 180 kg/s and eject the exhaust at a relative velocity of 5700 m/s. In reality, would start at 90° and decrease over time as the rocket ascends. However, we will consider the case where the rocket remains vertical (0 = 90°) throughout. You may also consider the engine firings as well as the jettisoning of stage A to be instant; that is, each engine fires at maximum burn from the moment they ignite, and the rocket switches to stage B at the moment stage A runs out of fuel. Using analysis for a variable system of particles, determine: (a) The speed at the moment stage A runs out of fuel (b) The speed at the moment stage B runs out of fuel (the max speed reached) 9 B S
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