Problem source

A projectile of unit mass
is fired in a northerly direction
from a point on a horizontal plain at speed $u$ and an angle 
$\theta$ above the horizontal.  It lands at a point $A$ on the plain.
In flight, the 
projectile experiences two forces: 
gravity, of magnitude $g$; and 
a horizontal force of
constant magnitude $f$ due to a wind blowing from North to South. Derive an
expression, in terms of $u$, $g$, $f$ and $\theta$ for the distance $OA$.
\begin{questionparts} 
\item Determine the angle $\alpha$ such that, for all $\theta>\alpha$,
the wind starts to blow the projectile back towards $O$ before it 
lands at $A$.
\item An identical projectile, which experiences the same forces,
 is fired from $O$ in a northerly direction
at speed $u$ and angle $45^\circ$ above the 
horizontal and lands at a point $B$ on the plain. Given that $\theta$ is
chosen to maximise $OA$, show that 
\[
\frac{OB}{OA} = \frac{ g-f}{\; \sqrt{g^2+f^2\;}- f \;\;}\;.
\]
Describe carefully the motion of the second  projectile when $f=g$.
\end{questionparts}