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highschoolmom2010
 one year ago
13. Using 6400 km as the radius of Earth, calculate how high above Earth’s surface you would have to be in order to weigh 1/16th of your current weight.
highschoolmom2010
 one year ago
13. Using 6400 km as the radius of Earth, calculate how high above Earth’s surface you would have to be in order to weigh 1/16th of your current weight.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You know this formula? \[F=\frac{ GMm }{ r^2 }\]

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0i know of it but not too much on how to apply it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok. in G is a gravitation constant, M is the mass of the bigger body (Earth) and m is the mass of the smaller one (you). This application is comparing your weight on the Earth to somewhere in space so you can make a ratio. \[F _{earth}=\frac{ GMm }{ r^2_{earth} }\] \[F _{orbit}=\frac{ GMm }{ r^2 }\] \[\frac{ F _{orbit} }{ F _{earth} }=\frac{ 1 }{ 16 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Does that make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435680564384:dw

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0ok i think i follow you

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok. were you able to solve for r?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The G, M, and m cancel so you're left with \[\frac{ 1 }{ 16 }=\frac{ 6400^2 }{ r^2 }\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the situation described in your problem is: dw:1435681788781:dw

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435681791475:dw well since you did it before i could figure out how to draw it YAY

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so we can write this: \[\begin{gathered} W = G\frac{{{M_T}m}}{{R_T^2}} \hfill \\ {W_1} = G\frac{{{M_T}m}}{{{{\left( {{R_T} + h} \right)}^2}}} \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lol :) so once you have that r, that's the distance from the center of the earth. You have to subtract 6400 from that to get your final answer

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now using your data we have to solve this equation: \[\frac{{{W_1}}}{W} = \frac{1}{{16}} = {\left( {\frac{{{R_T}}}{{{R_T} + h}}} \right)^2}\] please solve that equation for h, and you will get your answer, where: R_T is the radius of the Earth

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint, we have: \[\Large \frac{{{R_T}}}{{{R_T} + h}} = \frac{1}{4}\]

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0im actually confused now :/

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1after a simplification, we get: \[\Large 4{R_T} = {R_T} + h\] what is h?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you know how to solve the equation you wrote above?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you can cross multiply

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0i was understanding ok until after we simplified for r

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0at @Michele_Laino first reply threw me off

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435682627087:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that's just a slightly different way of doing it. she separated the earth's radius and the height, and I just kept it all as one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the benefit of her way is you don't have to subtract at the end

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435682797670:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0square 6400 first then multiply by 16 then take the square root

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1reassuming: the weight of a mass m which is locate h meters above the Earth's surface is: \[{W_1} = G\frac{{{M_T}m}}{{{{\left( {{R_T} + h} \right)}^2}}}\] whereas the weight of our mass m when it is located upon the Eart's surface is: \[W = G\frac{{{M_T}m}}{{R_T^2}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, using the data from your problem , we have to solve this equation: \[\frac{{{W_1}}}{W} = \frac{1}{{16}} = {\left( {\frac{{{R_T}}}{{{R_T} + h}}} \right)^2}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1which is equivalent to this one: \[\frac{{{R_T}}}{{{R_T} + h}} = \frac{1}{4}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1or to this one: \[4{R_T} = {R_T} + h\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1from which we get the requested height as below: \[\Large h = 3{R_T} = 3 \times 6400 = ...Km\]

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0oh ok 6400^2=40960000 40960000*16=655360000 \[\sqrt{655360000}=25600\] @peachpi

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0i hope i did it right that time

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes that's right. that's the distance from the center of the earth, so you have to subtract the radius of earth (6400) to get the distance from the surface.

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0so 256006400?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0there's your answer :)

highschoolmom2010
 one year ago
Best ResponseYou've already chosen the best response.0thank you :)
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