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Help with gravitation proof

  • Thread starter K29
  • Start date
  • #1
K29
108
0

Homework Statement


A rocket accelerates to speed v0 near the earth's surface,and then coasts upwards. Show that if
v0 = 2sqrt(gR)
where R is the Earth's radius, then very far from the earth the rockets speed will be
v = sqrt(2gR)


Homework Equations


The only equations I have thought of that may help are:
Escape Velocity:
v = sqrt(2GM/R)
Gravitational potential energy:
U= -GMm/r



The Attempt at a Solution


I have attempted using energy conservation and solving for v, however the answer appears far from that required.
This lead me to think that perhaps linear approximation may be required but I am unsure how I would apply (1+x)n = 1+nx for x<<1 in this problem.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
249
Welcome to PF!

Hi K29! Welcome to PF! :smile:

(have a square-root: √ :wink:)
A rocket accelerates to speed v0 near the earth's surface,and then coasts upwards. Show that if
v0 = 2sqrt(gR)
where R is the Earth's radius, then very far from the earth the rockets speed will be
v = sqrt(2gR)

The only equations I have thought of that may help are:
Escape Velocity:
v = sqrt(2GM/R)
Gravitational potential energy:
U= -GMm/r
Yes, those equations should do it …

but they use G, not g …

so what is the formula connecting G and g (and R)? :smile:
 
  • #3
K29
108
0
Ah yes. Thank you. All I needed to do was manipulate the final answer that I had from enegry conservations a tiny bit and then substitute that formula in

uhm as a new user,... am I meant to reply once I've got an answer??
I like the style of answering questions. Better than just copying an answer. "Help" is the way to go. At least that way I know where I've gone wrong
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
249
uhm as a new user,... am I meant to reply once I've got an answer??
I like the style of answering questions. Better than just copying an answer. "Help" is the way to go. At least that way I know where I've gone wrong
Hi K29!

Yes, it's friendlier if people reply. :smile:

Otherwise we tend to assume that they got a complete answer to the same question on another site, and never bothered with the hints from this site. :rolleyes:

The hints, btw, are the characteristic policy of PF … Greg Bernhardt :smile: reckons that members learn better if they have to do most of the work themselves!

See you around! :wink:
 
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