Motion described with differential equation

[ttchoubs]

1. http://i.imgur.com/3xya7IM.jpg




3. I curently do not understand how to jump to finding an acceleration due to gravity (in those terms asked) from the differential equations

 

[ChrisVer]

From the up eq, you can find its time (depending on g)... and for the down, you can do the same...
then you can solve for g since you know their summation...

 

[HallsofIvy]

From $dv/dt= -mg- kv$ you can get
$$\frac{dv}{mg+ kv}= -dt$$
Integrate both sides.