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
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Chapter6: Momentum And Collisions
Section: Chapter Questions
Problem 10WUE
Question
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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