Question

the figure shows that a bicyclist tips the cycle when making a turn. the angle, b, formed by the vertical direction and the bicycle, is called the banking angle. the banking angle varies inversely as the cycles turning radius. when the turning radius is 2.4 feet, the banking angle is 72°. what is the banking angle when the turning radius is 4.8 feet? the banking angle is \boxed{}° when the turning radius is 4.8 feet.

Explanation:

Step1: Write the inverse - variation equation

Since \(B\) varies inversely as \(r\), the equation is \(B=\frac{k}{r}\), where \(k\) is the constant of variation.
When \(r = 2.4\) and \(B=72\), substitute into the equation: \(72=\frac{k}{2.4}\).
Solve for \(k\): \(k = 72\times2.4=172.8\).

Step2: Find the value of \(B\) when \(r = 4.8\)

Substitute \(k = 172.8\) and \(r = 4.8\) into \(B=\frac{k}{r}\).
\(B=\frac{172.8}{4.8}\)
\(B = 36\)

Answer:

\(36\)