Question

the tires of a bicycle have radius 12.0 in. and are turning at the rate of 230 revolutions per min. see the figure. how fast is the bicycle traveling in miles per hour? (hint: 5280 ft = 1 mi)

given that the tires are on the ground, 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 $r=12.0$ inches, so $C = 2\pi(12)=24\pi$ inches.

Step2: Find the distance traveled per minute

The tire makes 230 revolutions per minute. The distance $d$ traveled per minute is the number of revolutions times the circumference. So $d = 230\times24\pi$ inches per minute. $d=5520\pi$ inches per minute.

Step3: Convert inches per minute to feet per minute

Since 1 foot = 12 inches, the distance in feet per minute is $\frac{5520\pi}{12}= 460\pi$ feet per minute.

Step4: Convert feet per minute to feet per hour

There are 60 minutes in an hour. So the distance in feet per hour is $460\pi\times60 = 27600\pi$ feet per hour.

Step5: Convert feet per hour to miles per hour

Since 5280 feet = 1 mile, the speed $v$ in miles per hour is $v=\frac{27600\pi}{5280}$.
$v=\frac{230\pi}{44}\approx 16.4$ miles per hour.

Answer:

$16.4$