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

A body is fired vertically from the ground of the Earth with a velocity [tex]v_0=1km/s[/tex]. If the gravitational force is not considered as constant and supposing that the Earth is a sphere of radius [tex]6371km[/tex],

a)Find the maximum height reached by the body.

b)Compare the previous result with the same experience if g is a constant. (That is [tex]9.8 m/s^2[/tex].)

2. Relevant equations[tex]r_{max}=\frac{1}{\frac{1}{r_0}-\frac{v_0^2}{2GM_E}}[/tex]

3. The attempt at a solutionI found the formula above in my class notes. If I understand it well, it gives "[tex]r_{max}[/tex]", which I interpret as the distance of a body from the center of the Earth. [tex]r_0[/tex] is the radius of the Earth and [tex]M_E[/tex] is the mass of the Earth.

I don't know how to find this formula so I think I will have to learn it by heart (sadly...). If you know how to reach to it, please let me know.

Now using the formula, I found that the projectile will reach [tex]6690.36km[/tex]! Oh wait.... this is the height from the center of the Earth, not the ground as I thought... So it's probably right then.

Because for the b) I get that it reach only [tex]51.020km[/tex], but it is from the ground of the Earth. Now that I think it makes about [tex]319 km[/tex] (if g is not a constant), I think it's too much, isn't it?

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# Homework Help: Projectile and gravitation problem

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