- #1

gasar8

- 63

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## Homework Statement

We release [itex] m_o = 1[/itex] kg object from h=1m height. How much does the Earth move (x)? I just need the comfirmation if I did correctly?

## Homework Equations

Conservation of momentum:

[itex] m_o v_o + m_E v_E = 0[/itex]

## The Attempt at a Solution

I wrote the energy conservation law as (beginning = end):

[tex] m_o g h = \frac{1}{2} m_o v_o^2 + \frac{1}{2} m_E v_E^2, [/tex]

and from momentum conservation got:

[tex] g h= \frac{1}{2} v_o^2 \bigg(1 + \frac{m_o}{m_E} \bigg), [/tex]

and now, I insert the free fall relation [itex]v_o = \sqrt{2g(h-x)}[/itex] from where I extract [itex]x[/itex] as:

[tex] x = h\frac{\frac{m_o}{m_E}}{1+\frac{m_o}{m_E}} .[/tex]

It seems reasonable, because it is something small.