Answer
The banking angle B is $32{}^\circ $when the turning radius is $r=3.5 feet$.
Work Step by Step
As the banking angle varies inversely as the cycle’s turning radius:
$B\propto \frac{1}{r}$
Using the proportionality constant k.
$B=\frac{k}{r}$
As $B=28{}^\circ $ and $r=4$ , we have
$\begin{align}
& B=\frac{k}{r} \\
& 28=\frac{k}{4} \\
& k=28(4) \\
& k=112
\end{align}$
Substitute the value of k in $B=\frac{k}{r}$
$B=\frac{112}{r}$
When $r=2.5$ then,
$B=\frac{112}{2.5}={{32}^{o}}$
