be the angle that
makes with the
-axis (positive in clockwise sense).
The thing to notice about this problem is that if you were to rotate the
coordinate system clockwise through an angle of
, to the new
coordinate system, the wind is then again parallel to the
-axis, so we arrive back at our original problem with the only difference being that our initial starting point for the trajectory is now at (
So we can treat this problem exactly the same as part (a)
up to the part where the initial conditions come in i.e. the limits of the integral in terms of
So at the starting point in the
frame coordinate system we have
so the integral becomes
are the dummy variables of integration in place of
From the integral we get:
Note this solution can be tidied up in various ways but I'll leave that to you.
Finally, the solution is in terms of the rotated coordinates
so it needs to be put back in terms of
using the transformation equations
The final result is then a big messy implicit equation in terms of
which I can't be bothered to late
so I'll leave to you to work out from the above!