Dynamics Problem? - reason for the cases described

Apparently, it's some sort of HW problem or exam. Where's the rest of it?

 

To me, these questions seem self-explanatory. If you have a specific question about something which is unclear, I'll try to help. But simply saying 'Explain this' is too vague.

 

Well, what happens when you shoot something out of a gun? Study the details given in section (c) and ask yourself if it would be safe for a man inside the spacecraft to be shot out of a gun.

It takes a certain velocity to achieve orbit. By siting the gun on the equator, how does this help achieve that velocity? What does the earth do all day?

 

(d)(i) Think about forces.
(d)(ii) The sun does not go around the earth each day, right?