Banked turn
SFx = Fc sin(q) + Ff cos(q) = mv2/r
SFy = Fc cos(q) - Ff sin(q) - mg = 0
Ff = mFc . Using the third equation, we can eliminate Ff in the first two:
Fc sin(q) + mFc cos(q) = mv2/r
Fc cos(q) - mFc sin(q) - mg = 0
We can now use the second equation to find Fc:
Fc = mg / [cos(q) - m sin(q)], and use this in the first equation to get:
v = [gr {sin(q)+m cos(q)} / {cos(q) - m sin(q)} ]1/2