Question

The figure shows that a bicyclist tips thecycle when making a turn. The angle, B,formed by the vertical direction and thebicycle, is called the banking angle. Thebanking angle varies inversely as the cycle'sturning radius. When the turning radius is4.2 feet, the banking angle is 68°. What isThe banking angle is when the turningradius is 5.6 feet.

Answer 1

$\theta\propto\frac{1}{r^{}}$$\begin{gathered} \text{adding a constant yields} \\ \theta=\frac{k}{r} \end{gathered}$$\begin{gathered} \text{but }\theta=\text{ 68 and r =4.2} \\ 68=k/4.2^{} \\ k\text{ =}285.6 \end{gathered}$$\begin{gathered} so\text{ } \\ \theta=\frac{285.6}{r} \end{gathered}$

Now looking for the banking angle when the turning radius is 5.6ft we substitute for r in the above equation

$\begin{gathered} \theta=\frac{285.6}{5.6^{}} \\ \theta=51^{\circ} \end{gathered}$