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Can you explain part c only Where does this formula come from and from where did they get VE Why do they then use it to substitute everything

Can you explain part c only Where does this formula come from and from where did they get VE Why do they then use it to substitute everything

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Can you explain part c only Where does this formula come from and from where did they get VE Why do they then use it to substitute everything
Problem 2- Rocket propulsion, two-stage rocket, escape velocity (a) A fully fueled rocket has an initial mass Mo, of which MF is the mass of the fuel alone. The rocket is launched vertical upward with initial velocity vo=0. Fuel is ejected with a given constant velocity, Vrel, and at burn-out time, t-tbo, the rocket reaches velocity Vbo-VE/2, where VE is the escape velocity from the surface of planet Earth. Find a formula for the burn-out time, tbo (no numbers needed here). (b) At burn-out time, a prearranged explosion separates the rocket into two parts, with part A stopped in midair by the prearranged explosion, while part B is propelled to a velocity VB>VE. Assuming a mass ratio, mA/MB-3, find the velocity of part B after the explosion. (c) Part B of the rocket now continues its travel into open space, moving radially outward from the center of the Earth, without additional propulsion. If prearranged explosion happened at an altitude h << re above the surface of the Earth, estimate the velocity of part B as it reaches a distance r = 10 re from the center of the Earth, with re the radius of planet Earth.
Transcribed Image Text:Problem 2- Rocket propulsion, two-stage rocket, escape velocity (a) A fully fueled rocket has an initial mass Mo, of which MF is the mass of the fuel alone. The rocket is launched vertical upward with initial velocity vo=0. Fuel is ejected with a given constant velocity, Vrel, and at burn-out time, t-tbo, the rocket reaches velocity Vbo-VE/2, where VE is the escape velocity from the surface of planet Earth. Find a formula for the burn-out time, tbo (no numbers needed here). (b) At burn-out time, a prearranged explosion separates the rocket into two parts, with part A stopped in midair by the prearranged explosion, while part B is propelled to a velocity VB>VE. Assuming a mass ratio, mA/MB-3, find the velocity of part B after the explosion. (c) Part B of the rocket now continues its travel into open space, moving radially outward from the center of the Earth, without additional propulsion. If prearranged explosion happened at an altitude h << re above the surface of the Earth, estimate the velocity of part B as it reaches a distance r = 10 re from the center of the Earth, with re the radius of planet Earth.
5 (C) Use conservation of energy! 2 1/2 MV 3 - GNOME GMB ME 10 TE re where v is the rebuity reached by the rocket when re 10 VE Now; 2 2G ME VE = 26M6 YE 2 2 V ₁² = 4 VE Therefore: -2- + 2V/² - 1/1/2 2 12 V= ²-31 VE 7x₂1² 2
Transcribed Image Text:5 (C) Use conservation of energy! 2 1/2 MV 3 - GNOME GMB ME 10 TE re where v is the rebuity reached by the rocket when re 10 VE Now; 2 2G ME VE = 26M6 YE 2 2 V ₁² = 4 VE Therefore: -2- + 2V/² - 1/1/2 2 12 V= ²-31 VE 7x₂1² 2
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