(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An object is dropped from an altitude of one Earth radius above Earth's surface. IfMis the mass of Earth andRis its radus, find the speed of the object just before it hits Earth.

2. Relevant equations

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

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

3. 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.

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# Falling object (gravity + kinematics)

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