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## Homework Statement

An object is dropped from an altitude of one Earth radius above Earth's surface. If

*M*is the mass of Earth and

*R*is its radus, find the speed of the object just before it hits Earth.

## Homework Equations

[tex]F_g=ma_g=\frac{GMm}{r^2}[/tex]

[tex]v^2=v_0^2+2ah[/tex]

## The Attempt at a Solution

[tex]F_g=\frac{GMm}{(2R)^2}=ma_g[/tex]

[tex]a_g=\frac{GM}{4R^2}[/tex]

Now, plug that into the kintematics equation and get

[tex]v^2=0+2(\frac{GM}{4R^2})R[/tex]

[tex]v=\sqrt{\frac{GM}{2R}}[/tex]

But the correct answer is given as [tex]\sqrt{\frac{GM}{R}}[/tex], and I can't find my error.