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GOsuchessplayer
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Homework Statement
An Object is fired vertically upward from the surface of the Earth ( of radius RE ) with an initial speed vi that is comparable to but less than the escape speed vesc
Show that the object attains a maximum height h given by h=[tex]\stackrel{R_{E}v^{2}_{i}}{v^{2}_{esc}-v^{2}_{i}}[/tex]
Homework Equations
The Attempt at a Solution
I have the solution but I am confused with a step.
Here is the solution provided up until the step on which I am confused:
[tex](K+U_{g})_{f}[/tex]=[tex](K+U_{g})_{f}[/tex]
[tex]\stackrel{1}{2}[/tex]m[tex]v^{2}_{i}[/tex] - [tex]\stackrel{GmM_{E}}{R_{E}}[/tex] = 0 - [tex]\stackrel{GmM_{E}}{R_{E}+h}[/tex]
where [tex]\stackrel{1}{2}[/tex]m[tex]v^{2}_{esc}[/tex]= [tex]\stackrel{GmM_{E}}{R_{E}}[/tex]
Then[tex]\stackrel{1}{2}[/tex][tex]v^{2}_{i}[/tex] - [tex]\stackrel{1}{2}[/tex][tex]v^{2}_{esc}[/tex]= -[tex]\stackrel{1}{2}[/tex][tex]v^{2}_{esc}[/tex] ([tex]\stackrel{R_{E}}{R_{E}+h}[/tex])
So the jump I am confused about is the equation that follows the "Then" Statement. I'm not sure why this is true.
(sorry for the poor look of the equations. Hopefully its readable, I wasn't sure how to make fractions.)
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