Variations of model

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​ cycle's turning radius. When the turning radius is

4

​feet, the banking angle is

33

degrees.

What is the banking angle when the turning radius is

5.5

​feet?

Answer 1

I have an issue with this problem since it doesn't factor in all the things that actually goes into calculating the banking angle... but I assume they just want you to use the knowledge of what "inversely" would represent here.

If something is inversely related, then as one thing goes up, another thing goes down. Since they don't give you proportions, it is safe to assume that they mean the system is Inversely Proportional (when one value decreases at the same rate that the other increases). This would mean if one went up by 20%, the other would go down by 20%.

Let the following be set :

r = radius of the turn

a = angle of the turn

x = % of change

r1 = 4

a1 = 33

r2 = 5.5 = r1*x = 4*x

5.5 / 4 = x

1.375 = x

a2 = a1 / x = 33 / 1.375

a2 = 24 feet

I'm not sure if this is 100% correct, but this is my best guess! the Radius increased 37.5% & the Banking Angle decreased 37.5%.

Answer 2

banking angle = k/turning radius

33=k/4 =>k=132

therefore

banking angle = 132/5.5

You do the arithmetic!