Microsoft Internet Explorer 9 offline installer (32 and 64-bit)
Microsoft Internet Explorer 9 Setup File
Installing Internet Explorer 9 Offline

Category:Internet ExplorerQ:

Moving body with a circular velocity

This should be an easy question, but I’ve been stuck on this for a while. My answer to this question is giving me a = 1. Which is wrong I think, as shouldn’t the distance moved increase as $r$ increases. Thanks in advance.

A:

Newton’s second law of motion says, $$F=ma$$ where $F$ is the force on the body, $m$ is its mass and $a$ is its acceleration. Assuming the «force» is the force of gravity acting on the body, then $$F=-m\frac{GMm}{r^2}$$ where $G$ is the gravitational constant and $M$ is the mass of the earth. This is the force per unit mass of the body, so we can divide by the mass, $m$, to get $a=-GM/r^2$.
If you want a distance per unit time, you can use the equation $$v=\frac{dr}{dt}=\frac{dr}{da}\frac{da}{dt}=\frac{dr}{da}\frac{d^2r}{dt^2}$$ where $v$ is the velocity of the body. This gives you the velocity of the body, $\frac{dr}{da}$, in terms of the acceleration of the body, $a$. Then plug that in to Newton’s second law above to get $$F=\frac{GM}{r^2}\left(\frac{dr}{da}\right)^2$$ from which you can get the distance $dr$ traveled per unit time.

Q:

How do I find the subdomain from an array of urls?

The title pretty much says it all, how would I get the first subdomain from this array?
array (size=3)
0 =>
array (size=5)
‘domain’ => string ‘www.site.com’ (length=12)
‘webroot’ => string ‘htdocs’ (length=5)

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