Answer
$137.03 \ m/s$
Work Step by Step
We know that the y-forces cancel out, for the height of the plane is constant throughout the bank. Thus, we find:
$mg = F_n cos\theta$
We know that the x-component of the normal force due to the air is the centripetal force, so we find:
$F_nsin\theta=\frac{mv^2}{r}$
Combining these equations gives:
$mg = \frac{mv^2}{rtan\theta}$
This means that the velocity is:
$v=\sqrt{grtan\theta}=\sqrt{(9.81)(3600)(tan28)}=137.03 \ m/s$
