1. Convert Units

* Frequency: We need to convert Hz (Hertz) to revolutions per second (rps). 1 Hz = 1 rps, so the frequency is already in the correct units.

* Linear Speed: Convert miles per second to meters per second (m/s).

* 1 mile = 1609.34 meters

* 20.0 miles/second * (1609.34 meters/mile) = 32186.8 m/s

2. Relate Linear Speed, Frequency, and Radius

The relationship between linear speed (v), frequency (f), and radius (r) of an object moving in a circle is:

v = 2πrf

3. Solve for Radius

* Rearrange the equation to solve for radius (r):

r = v / (2πf)

* Plug in the values:

r = (32186.8 m/s) / (2π * 11 Hz)

* Calculate the radius:

r ≈ 466.8 meters

Therefore, the radius of the car tire is approximately 466.8 meters.

Important Note: This answer seems very large for a car tire. It's likely there's an error in the given information (either the frequency or the linear speed is unrealistic for a car tire). This problem highlights the importance of checking for reasonable answers when working with physical quantities.