Question

1. the tires of a bicycle have radius 12.0 in. and are turning at the rate of 200 revolutions per min. see the figure. how fast is the bicycle traveling in miles per hour? (hint: 5280 ft = 1 mi) how fast is the bicycle traveling? mph (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Calculate the circumference of the tire

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(r=12.0\) in, then \(C = 2\pi\times12.0=24\pi\) in.

Step2: Calculate the distance traveled per minute

The tire makes 200 revolutions per minute. The distance traveled per minute \(d_{min}\) is the number of revolutions per minute times the circumference. So \(d_{min}=200\times24\pi\) in. \(d_{min}=4800\pi\) in.

Step3: Convert inches per minute to miles per hour

First, convert inches to feet. Since \(1\) foot \( = 12\) inches, then \(d_{min}=\frac{4800\pi}{12}\) ft \( = 400\pi\) ft.
Then convert feet to miles. Since \(1\) mile \(=5280\) ft, the distance per minute in miles is \(d_{min - mi}=\frac{400\pi}{5280}\) miles.
To get the distance per hour, multiply by 60 (because there are 60 minutes in an hour). So \(v=\frac{400\pi\times60}{5280}\) mph.

$$v=\frac{24000\pi}{5280}\approx\frac{24000\times3.14159}{5280}\approx\frac{75398.16}{5280}\approx14.3$$

Answer:

\(14.3\)