Question

the tires of a bicycle have radius 12.0 in. and are turning at the rate of 225 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? \\(\square\\) mph (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Find the circumference of the tire

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

Step2: Find the distance traveled per minute

The tire makes 225 revolutions per minute. Each revolution is the circumference, so distance per minute \( d_{min}=225\times24\pi \) inches. Calculate that: \( 225\times24\pi = 5400\pi \) inches per minute.

Step3: Convert inches per minute to feet per minute

Since 1 foot = 12 inches, divide by 12: \( d_{min(ft)}=\frac{5400\pi}{12}=450\pi \) feet per minute.

Step4: Convert feet per minute to miles per hour

First, convert minutes to hours: 1 hour = 60 minutes, so multiply by 60: \( d_{hour(ft)} = 450\pi\times60 = 27000\pi \) feet per hour. Then, since 1 mile = 5280 feet, divide by 5280: \( d_{hour(miles)}=\frac{27000\pi}{5280} \). Calculate this value: \( \frac{27000\pi}{5280}\approx\frac{27000\times3.1416}{5280}\approx\frac{84823.2}{5280}\approx16.1 \) (rounded to the nearest tenth).

Answer:

16.1